publications | Adrián Amor Martín

JCR journals

2024

A Rigorous Code Verification Process of the Domain Decomposition Method in a Finite Element Method For Electromagnetics

Adrian Amor-Martin, Luis E. Garcia-Castillo, Laszlo L. Toth, and 2 more authors

IEEE Transactions on Antennas and Propagation, 2024

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The finite element method (FEM) has benefited recently from the introduction of the domain decomposition method (DDM), especially to tackle large-scale problems. Many versions of DDM may be found in the literature, and almost none of them have used a rigorous approach to show the accuracy of the formulation. Here, we suggest the use of the method of manufactured solutions (MMS) to introduce DDM into a FEM code. This approach also allows us to debug the demanding coding process of the method. First, we introduce the mandatory operators used for DDM to construct second-order absorbing boundary conditions. Then, we use these results to show the correct implementation of DDM with basis functions up to fourth order for tetrahedra, triangular prisms, and hexahedra, obtaining the convergence rates predicted by the classic FEM theory. Finally, we illustrate how to use MMS to test different formulations, assessing the effect of using different spaces and orders for the arising ancillary variables.
Hierarchical Universal Matrices for Curvilinear Tetrahedral H(Curl) Finite Elements with Inhomogeneous Material Properties

Laszlo L. Toth, Adrian Amor-Martin, and Romanus Dyczij-Edlinger

IEEE Transactions on Antennas and Propagation, 2024

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A general method for calculating the mass and stiffness matrices of H(curl)-conforming finite elements is pro- posed. It applies to curvilinear geometries geometry and/or inhomogeneous materials, preserves the nullspace of the curl operator, and is computationally efficient. In the finite element integrals, the terms incorporating the effects of geometry and materials are expanded in a series of multivariate polynomials. As a result, the element matrices can always be integrated analytically by means of predefined universal matrices. The mapping from the reference element to the physical configuration is done performed by suitable forms of the Piola transformation the Piola transformations so that the resulting finite element bases are guaranteed to preserve the nullspace of the curl operator. A mathematical proof, including the curvilinear case, is included. The suggested approach features a representation limit: When the metric expansion is continued beyond a critical order, which is determined by the order of the finite element basis, the truncation error becomes zero. Hence, the number of universal matrices is bounded, and the sole source of error is the numerical calculation of the expansion coefficients for the metric terms. The method is validated by numerical examples, and its computational efficiency is demonstrated by a comparison to competing approaches.
A priori verification method for curl-conforming basis functions in simplices

Adrian Amor-Martin, and Luis E. Garcia-Castillo

Mathematical Methods in the Applied Sciences, 2024

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The construction of (hierarchical) curl-conforming basis functions has been a hot topic in the last decades in the finite element community. Especially, functions applied to simplices have been quite popular after the work by Nédélec in 1980. Many mixed-order and full-order families have been provided in the last years, but sometimes, it is difficult to assess if they belong to the original space proposed by Nédélec (especially when orthogonalization procedures are applied). Here, a tool to determine if a family of basis functions belongs to the Nédélec space is provided. Since affine coordinates are the most frequent choice for simplices, particularities about its use with this kind of coordinates are detailed. A detailed survey of existing families is provided, and the practical application of the tool to a representative set of these families is discussed. The tool is also available for the community in a public repository.
Urban Sound Classification Using Neural Networks on Embedded FPGAs

Jose A. Belloch, Raúl Coronado, Óscar Valls, and 6 more authors

The Journal of Supercomputing, 2024

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The sound classification assisted by neural networks has led to high-accurate results. A high number of different applications uses this kind of sound classification, such as: control and monitoring of the number of vehicles on roads or identifying different types of animals in natural environments. While traditional acoustic processing applications have been developed taking into account high-throughput computing platforms equipped with expensive multichannel audio interfaces, the IoT paradigm demands the use of more flexible and energy-efficient systems. Although there exist software-based platforms devoted to implementing general neural networks, they are not optimized for sound classification leading to the waste of energy and computational resources. Here, we have used FPGAs to develop an ad-hoc system where only the required hardware for our application is synthesized, obtaining faster and cheaper (in terms of energy) circuits. The results show that our developments accelerates by a factor of 35 with respect to a software-based implementation on a Raspberry Pi.
Fully Metallic Geodesic Lenses as Analog Electromagnetic Models of Static and Spherically Symmetric Gravitational Fields

Enderson Falcón-Gómez, Vittorio De Falco, Kerlos Atia Abdalmalak, and 4 more authors

Physical Review D, Aug 2024

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We demonstrate that a fully metallic and air-filled geodesic waveguide can be employed as an analog electromagnetic model of a static and spherically symmetric gravitational field. By following the Plebanski formalism, a space-time metric of the aforementioned type is first encoded into the electromagnetic properties of a flat space-time region in the form of an isotropic and radially varying refractive index distribution. Then, a three-dimensional, air-filled, and axially symmetric waveguide, composed of two equally spaced and curved metallic surfaces, is employed. Its shape is tailored such that the effective paths, followed by transverse electromagnetic beams of microwave radiation within this waveguide, result equivalent to null-geodesics taking place in the aforementioned refractive medium. This strategy avoids the need for a refractive medium, although it only allows to reproduce the space-time metric on the invariant plane. Two analog electromagnetic models of gravity, using the proposed approach, are designed to reproduce the metric of both a Schwarzschild black hole and a Morris-Thorne wormhole. The results from full-wave simulations demonstrate that a one-dimensional Gaussian beam faithfully follows a path completely equivalent to general relativistic null geodesics with a mean relative error within 4%.

2023

Meshing strategies for 3d geo-electromagnetic modeling in the presence of metallic infrastructure

Octavio Castillo-Reyes, Paula Rulff, Evan Schankee Um, and 1 more author

Computational Geosciences, Aug 2023

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In 3D geo-electromagnetic modeling, an adequate discretisation of the modeling domain is crucial to obtain accurate forward responses and reliable inversion results while reducing the computational cost. This paper investigates the mesh design for subsurface models, including steel-cased wells, which is relevant for many exploration settings but still remains a numerically challenging task. Applying a goal-oriented mesh refinement technique and subsequent calculations with the high-order edge finite element method, simulations of 3D controlled-source electromagnetic models in the presence of metallic infrastructure are performed. Two test models are considered, each needing a distinct version of approximation methods to incorporate the conductive steel casings of the included wells. The influence of mesh quality, goal-oriented meshing, and high-order approximations on problem sizes, computational cost, and accuracy of electromagnetic responses is investigated. The main insights of our work are: (a) the applied numerical schemes can mitigate the computational burden of geo-electromagnetic modeling in the presence of steel artifacts; (b) investigating the processes driving the meshing of models with embedded metallic infrastructures can lead to adequate strategies to deal with the inversion of such electromagnetic data sets. Based on the modeling results and analyses conducted, general recommendations for modeling strategies are proposed when performing simulations for challenging steel infrastructure scenarios.
Second-Order Nédélec Curl-Conforming Hexahedral Element for Computational Electromagnetics

Adrian Amor-Martin, and Luis E. Garcia-Castillo

IEEE Transactions on Antennas and Propagation, Aug 2023

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We follow a systematic approach to obtain mixed-order curl-conforming basis functions for the hexahedron that are compatible with basis functions for tetrahedra and triangular prisms previously published. The approach is mathematically sound since we obtain the functions as the dual basis with respect to properly discretized Nédélec degrees of freedom. Simple to use and well-conditioned bases without the need for added orthogonalization procedures are obtained. We provide simple closed-form expressions for second-order basis functions in a reference hexahedron in terms of integer coefficients and monomials. The expressions are ready to use as long as the appropriate geometric mappings are made. We apply the Method of Manufactured Solutions to a finite element double curl vector wave formulation for verification purposes; specifically, we make a study of the non-symmetrical structure of the corresponding tensor product finite element space. We also solve generalized eigenvalue problems for well-known cavities. We provide the open-source code for generating the coefficients, evaluating the basis functions, and computing the finite element matrices involved in some of the numerical solutions shown in the paper.
Interaction between Linear Polarized Plane Gravitational Waves and a Plane Electromagnetic Wave in the Electromagnetic-Gravity Analogue

Enderson Falcón-Gómez, Vittorio De Falco, Kerlos Atia Abdalmalak, and 4 more authors

Physical Review D, Mar 2023

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In this manuscript, we present an alternative method for calculating null geodesics in General Static Isotropic Metrics in General Relativity and Extended Theories of Gravity. By applying a conformal transformation, we are able to consider an analogue gravity model, where curvature is encoded in the dielectric and magnetic properties of a medium. In other words, we pass from curved to flat space-times, where instead of the Einstein field equations, the Maxwell equations are solved. Within this geometrical background, the photon geodesics are calculated. Then, given different black hole and wormhole metrics, we apply this method obtaining an excellent agreement with respect to the exact solutions in the original gravity framework by committing angular deviations below \\3\^{∘}\\. Finally, we provide the image of a Schwarzschild black hole surrounded by a thin accretion disk, and the apparent image of a Morris and Thorne-like WH wormhole within an angular discrepancy below \\4\^{∘}\\.

2022

Strategies to Parallelize a Finite Element Mesh Truncation Technique on Multi-Core and Many-Core Architectures

Jose M. Badia, Adrian Amor-Martin, Jose A. Belloch, and 1 more author

The Journal of Supercomputing, Dec 2022

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Achieving maximum parallel performance on multi-core CPUs and many-core GPUs is a challenging task depending on multiple factors. These include, for example, the number and granularity of the computations or the use of the memories of the devices. In this paper, we assess those factors by evaluating and comparing different parallelizations of the same problem on a multiprocessor containing a CPU with 40 cores and four P100 GPUs with Pascal architecture. We use, as study case, the convolutional operation behind a non-standard finite element mesh truncation technique in the context of open region electromagnetic wave propagation problems. A total of six parallel algorithms implemented using OpenMP and CUDA have been used to carry out the comparison by leveraging the same levels of parallelism on both types of platforms. Three of the algorithms are presented for the first time in this paper, including a multi-GPU method, and two others are improved versions of algorithms previously developed by some of the authors. This paper presents a thorough experimental evaluation of the parallel algorithms on a radar cross-sectional prediction problem. Results show that performance obtained on the GPU clearly overcomes those obtained in the CPU, much more so if we use multiple GPUs to distribute both data and computations. Accelerations close to 30 have been obtained on the CPU, while with the multi-GPU version accelerations larger than 250 have been achieved.
Propagation of Light in the Presence of Gravity Generated by Static and Spherically Symmetric Curved Space-Times Using Maxwell Equations

Enderson Falcón-Gómez, Adrián Amor-Martín, Valentín De La Rubia, and 3 more authors

The European Physical Journal C, Dec 2022

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In this manuscript, we present an alternative method for calculating null geodesics in General Static Isotropic Metrics in General Relativity and Extended Theories of Gravity. By applying a conformal transformation, we are able to consider an analogue gravity model, where curvature is encoded in the dielectric and magnetic properties of a medium. In other words, we pass from curved to flat space-times, where instead of the Einstein field equations, the Maxwell equations are solved. Within this geometrical background, the photon geodesics are calculated. Then, given different black hole and wormhole metrics, we apply this method obtaining an excellent agreement with respect to the exact solutions in the original gravity framework by committing angular deviations below \\3\^{∘}\\. Finally, we provide the image of a Schwarzschild black hole surrounded by a thin accretion disk, and the apparent image of a Morris and Thorne-like WH wormhole within an angular discrepancy below \\4\^{∘}\\.
Tailored Meshing for Parallel 3D Electromagnetic Modeling Using High-Order Edge Elements

Octavio Castillo-Reyes, Adrian Amor-Martin, Arnaud Botella, and 2 more authors

Journal of Computational Science, Aug 2022

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We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised h+p refinement approaches on massively parallel computers. Our high-order h+p refinement strategy is based on and extends the PETGEM code. We focus on the performance study in terms of accuracy, convergence rate, and computational effort to solve real-life 3D setups based on synthetic and experimental data for energy reservoir characterization. These test cases show variable resolution discretization needs and realistic physical parameters. In general, our numerical results are consistent theoretically. The use of h-adapted meshes was efficient to achieve a certain accuracy level in the synthetic EM responses. Regarding global p-refinement, p=2 exhibits the best accuracy/performance trade-off. Selective p-refinement might offer a better compromise between accuracy and computational cost. However, for p-refinement at different entities, the best refinement scheme consists of using p=3 at the volume level with p=1 at faces and edges. Thus, p-refinement can be competitive if applied hierarchically. Nevertheless, we acknowledge that the performance of our supervised h+p refinement strategy depends on the input model (e.g., conductivity, frequency, domain decomposition strategy, among others). Whatever the chosen configuration, our numerical results provide an in-depth understanding of EM modeling’s pros and cons when supervised h+p refinement schemes are applied.
3D Magnetotelluric Modeling Using High-Order Tetrahedral Nédélec Elements on Massively Parallel Computing Platforms

Octavio Castillo-Reyes, David Modesto, Pilar Queralt, and 5 more authors

Computers & Geosciences, Jan 2022

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We present a routine for 3D magnetotelluric (MT) modeling based upon high-order edge finite element method (HEFEM), tailored and unstructured tetrahedral meshes, and high-performance computing (HPC). This implementation extends the PETGEM modeller capabilities, initially developed for active-source electromagnetic methods in frequency-domain. We assess the accuracy, robustness, and performance of the code using a set of reference models developed by the MT community in well-known reported workshops. The scale and geological properties of these 3D MT setups are challenging, making them ideal for addressing a rigorous validation. Our numerical assessment proves that this new algorithm can produce the expected solutions for arbitrarily 3D MT models. Also, our extensive experimental results reveal four main insights: (1) high-order discretizations in conjunction with tailored meshes can offer excellent accuracy; (2) a rigorous mesh design based on the skin-depth principle can be beneficial for the solution of the 3D MT problem in terms of numerical accuracy and run-time; (3) high-order polynomial basis functions achieve better speed-up and parallel efficiency ratios than low-order polynomial basis functions on cutting-edge HPC platforms; (4) a triple helix approach based on HEFEM, tailored meshes, and HPC can be extremely competitive for the solution of realistic and complex 3D MT models and geophysical electromagnetics in general.

2021

Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method

Adrian Amor-Martin, and Luis E. Garcia-Castillo

Applied Sciences, Jan 2021

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Test-Driven Development of a Substructuring Technique for the Analysis of Electromagnetic Finite Periodic Structures

Ignacio Martínez-Fernández, Adrian Amor-Martin, and Luis E. Garcia-Castillo

Applied Sciences, Dec 2021

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In this paper, we follow the Test-Driven Development (TDD) paradigm in the development of an in-house code to allow for the finite element analysis of finite periodic type electromagnetic structures (e.g., antenna arrays, metamaterials, and several relevant electromagnetic problems). We use unit and integration tests, system tests (using the Method of Manufactured Solutions—MMS), and application tests (smoke, performance, and validation tests) to increase the reliability of the code and to shorten its development cycle. We apply substructuring techniques based on the definition of a unit cell to benefit from the repeatability of the problem and speed up the computations. Specifically, we propose an approach to model the problem using only one type of Schur complement which has advantages concerning other substructuring techniques.
Study of Accuracy of a Non-Conformal Finite Element Domain Decomposition Method

Adrian Amor-Martin, Luis E. Garcia-Castillo, and Jin-Fa Lee

Journal of Computational Physics, Dec 2021

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Domain Decomposition Methods (DDM) have been widely used in the Computational Electromagnetics (CEM) community in the last years to tackle large-scale problems with Finite Element Methods (FEM). Non-conformal DDM is more flexible (e.g., independently created meshes for different parts of the problem under analysis are supported) but may introduce an approximation error. In this communication, a thorough study of the accuracy of the solutions when using non-conformal DDM is presented. Three experiments are realized showing the verification of the implementation and that the accuracy is acceptable with different numbers of discontinuities in the propagation direction and various aspect ratios of the mesh on the interface. The numerical results use three different shapes (tetrahedra, prisms, and hexahedra) and up to order three in the basis functions that approximate the field. These studies are relevant for the introduction of non-conformal DDM with real problems or scalable (in the parallel sense) implementation of adaptive mesh techniques.

2020

A Testbench of Arbitrary Accuracy for Electromagnetic Simulations

Adrian Amor‐Martin

International Journal of RF and Microwave Computer-Aided Engineering, Dec 2020

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Several electromagnetic problems for verification purposes in computational electromagnetics are introduced. Details about the formulation of a generalized eigenvalue problem for non-lossy and lossy materials are provided to obtain a fast and ready-to-use way of verification. Codes written using the symbolic toolbox from MATLAB are detailed to obtain an arbitrary accuracy for the proposed problems. Finally, numerical results in a finite element method code are presented together with the analytical values to show the accuracy of the code proposed.
GPU Acceleration of a Non-Standard Finite Element Mesh Truncation Technique for Electromagnetics

José M. Badía, Adrian Amor-Martin, Jose A. Belloch, and 1 more author

IEEE Access, Dec 2020

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The emergence of General Purpose Graphics Processing Units (GPGPUs) provides new opportunities to accelerate applications involving a large number of regular computations. However, properly leveraging the computational resources of graphical processors is a very challenging task. In this paper, we use this kind of device to parallelize FE-IIEE (Finite Element-Iterative Integral Equation Evaluation), a non-standard finite element mesh truncation technique introduced by two of the authors. This application is computationally very demanding due to the amount, size and complexity of the data involved in the procedure. Besides, an efficient implementation becomes even more difficult if the parallelization has to maintain the complex workflow of the original code. The proposed implementation using CUDA applies different optimization techniques to improve performance. These include leveraging the fastest memories of the GPU and increasing the granularity of the computations to reduce the impact of memory access. We have applied our parallel algorithm to two real radiation and scattering problems demonstrating speedups higher than 140 on a state-of-the-art GPU.

2019

Construction of Higher-Order Curl-Conforming Finite Elements and Its Assembly

Adrian Amor-Martin, and Luis E. Garcia-Castillo

International Journal of RF and Microwave Computer-Aided Engineering, Dec 2019

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Different choices are available when constructing vector finite element bases in real coordinates. In this communication, two different designs of higher‐order curl‐conforming basis functions are introduced and explained, showing the particularities of its assembly. Tetrahedra and hexahedra are used as element shapes to assess the effect of triangular and quadrilateral faces on the two considered constructions of basis functions. A comparison of their robustness in terms of the condition number of the finite element matrices for a number of distortions is included.
On the Use of Many-Core Machines for the Acceleration of a Mesh Truncation Technique for FEM

Jose A. Belloch, Adrian Amor-Martin, Daniel Garcia-Donoro, and 2 more authors

The Journal of Supercomputing, Dec 2019

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Finite element method (FEM) has been used for years for radiation problems in the field of electromagnetism. To tackle problems of this kind, mesh truncation techniques are required, which may lead to the use of high computational resources. In fact, electrically large radiation problems can only be tackled using massively parallel computational resources. Different types of multi-core machines are commonly employed in diverse fields of science for accelerating a number of applications. However, properly managing their computational resources becomes a very challenging task. On the one hand, we present a hybrid message passing interface + OpenMP-based acceleration of a mesh truncation technique included in a FEM code for electromagnetism in a high-performance computing cluster equipped with 140 compute nodes. Results show that we obtain about 85% of the theoretical maximum speedup of the machine. On the other hand, a graphics processing unit has been used to accelerate one of the parts that presents high fine-grain parallelism.

2018

Supervised Machine Learning Using Encrypted Training Data

Francisco-Javier González-Serrano, Adrian Amor-Martin, and Jorge Casamayón-Antón

International Journal of Information Security, Dec 2018

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Preservation of privacy in data mining and machine learning has emerged as an absolute prerequisite in many practical scenarios, especially when the processing of sensitive data is outsourced to an external third party. Currently, privacy preservation methods are mainly based on randomization and/or perturbation, secure multiparty computations and cryptographic methods. In this paper, we take advantage of the partial homomorphic property of some cryptosystems to train simple machine learning models with encrypted data. Our basic scenario has three parties: multiple Data Owners, which provide encrypted training examples; the Algorithm Owner (or Application), which processes them to adjust the parameters of its models; and a semi-trusted third party, which provides privacy and secure computation services to the Application in some operations not supported by the homomorphic cryptosystem. In particular, we focus on two issues: the use of multiple-key cryptosystems, and the impact of the quantization of real-valued input data required before encryption. In addition, we develop primitives based on the outsourcing of a reduced set of operations that allows to implement general machine learning algorithms using efficient dedicated hardware. As applications, we consider the training of classifiers using privacy-protected data and the tracking of a moving target using encrypted distance measurements.

2017

Training Support Vector Machines with Privacy-Protected Data

Francisco-Javier González-Serrano, Ángel Navia-Vázquez, and Adrian Amor-Martin

Pattern Recognition, Dec 2017

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In this paper, we address a machine learning task using encrypted training data. Our basic scenario has three parties: Data Owners, who own private data; an Application, which wants to train and use an arbitrary machine learning model on the Users’ data; and an Authorization Server, which provides Data Owners with public and secret keys of a partial homomorphic cryptosystem (that protects the privacy of their data), authorizes the Application to get access to the encrypted data, and assists it in those computations not supported by the partial homomorphism. As machine learning model, we have selected the Support Vector Machine (SVM) due to its excellent performance in supervised classification tasks. We evaluate two well known SVM algorithms, and we also propose a new semiparametric SVM scheme better suited for the privacy-protected scenario. At the end of the paper, a performance analysis regarding the accuracy and the complexity of the developed algorithms and protocols is presented.

2016

Second-Order Nédélec Curl-Conforming Prismatic Element for Computational Electromagnetics

Adrian Amor-Martin, Luis E. Garcia-Castillo, and Daniel Garcia-Donoro

IEEE Transactions on Antennas and Propagation, Dec 2016

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A systematic approach to obtaining mixed-order curl-conforming basis functions for a triangular prism is presented; focus is made on the second-order case. Space of functions for the prism is given. Basis functions are obtained as the dual basis with respect to suitably discretized Nédélec degrees of freedom functionals acting on elements of the space. Thus, the linear independence of the basis functions is assured while the belonging of the basis to the a priori given space of functions is guaranteed. Different strategies for the finite element assembly of the basis are discussed. Numerical results showing the verification procedure of the correctness of the implemented basis functions are given. Numerical results about sensibility of the condition number of the basis obtained concerning the quality of the elements of the mesh are also shown. Comparison with other representative sets of basis functions for prisms is included.
Analysis of Planar Microwave Devices Using Higher Order Curl-Conforming Triangular Prismatic Finite Elements

Daniel Garcia-Donoro, Sioweng Ting, Adrian Amor-Martin, and 1 more author

Microwave and Optical Technology Letters, Dec 2016

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The evaluation of the accuracy and performance of a higher‐order curl‐conforming triangular prismatic finite element is carried out in this article. The triangular prismatic finite element proposed by the authors is tested by simulating real microwave devices in planar technology. The results obtained using this prismatic element are compared with those obtained using the finite element method reference commercial software HFSS that makes use of higher‐order tetrahedral finite elements. Conclusions about the use of this prismatic element for the analysis of planar microwave devices are given.

2015

Posidonia: A Tool for HPC and Remote Scientific Simulations [EM Programmer’s Notebook]

Adrian Amor-Martin, Ignacio Martinez-Fernandez, and Luis E. Garcia-Castillo

IEEE Antennas and Propagation Magazine, Dec 2015

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This article presents a software tool named Posidonia. Posidonia removes the barrier to entry for the novice user of high-performance computing (HPC) systems, and remote scientific simulations in general, while increasing productivity of the experienced user. Posidonia manages communication with the remote computer system and interacts with its batch system (job scheduler). In addition, Posidonia keeps a history repository of simulations. The software also comes in several versions, including desktop, Android, and web interfaces; fully integration with given simulators/solvers has also been developed. We have designed an implementation within the paradigm of object orientation using Java and as a layered architecture that provides increased code reuse. In this article, we show the functionality, usability, and software architecture of Posidonia.

Ph.D. thesis

2018

Advanced techniques in scientific computing: application to electromagnetics

Adrian Amor-Martin

2018

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In the last years, more and more accurate and demanding simulations of radiofrequency components in a system of communications are requested by the community. To address this need, some techniques have been introduced in finite element methods (FEM), such as hp adaptivity (which estimates the error in the problem and generates tailored meshes to achieve more accuracy with less unknowns than in the case of uniformly refined meshes) or domain decomposition methods (DDM, consisting of dividing the whole problem into more manageable subdomains which can be solved in parallel). The performance of the adaptivity techniques is good up to two dimensions, whereas for three dimensions the generation time of the adapted meshes may be prohibitive. On the other hand, large scale simulations have been reported with DDM becoming a hot topic in the computational electromagnetics community. The main objective of this dissertation is to study the viability of scalable (in terms of parallel performance) algorithms combining nonconformal DDM and automatic adaptivity in three dimensions. Specifically, the adaptivity algorithms might be run in each subdomain independently. This combination has not been detailed in the literature and a proof of concept is discussed in this work. Thus, three building blocks must be introduced: i) basis functions for the finite elements which support non-uniform approximation orders p; ii) non-conformal and non-overlapping DDM; and iii) adaptivity algorithms in 3D. In this work, these three building blocks have been successfully introduced in a FEM code with a systematic procedure based on the method of manufactured solutions (MMS). Moreover, a three-level parallelization (at the algorithm level, with DDM; at the process level, with message passing interface (MPI), and at the thread level, with OpenMP) has been developed using the paradigm of modular programming which eases the software maintenance and the introduction of new features. Regarding first building block, a family of basis functions which follows a sound mathematical approach to expand the correct space of functions is developed and particularized for triangular prisms. Also, to ease the introduction of different approximation orders in the same mesh, hierarchical basis functions from other authors are used as a black box. With respect to DDM, a thorough study of the error introduced by the non-conformal interfaces between subdomains is required for the adaptivity algorithm. Thus, a quantitative analysis is detailed including non-conformalities generated by independent refinements in neighbor subdomains. This error has not been assessed with detail in the literature and it is a key factor for the adaptivity algorithm to perform properly. An adaptivity algorithm with triangular prisms is also developed and special considerations for the implementation are explained. Finally, on top of these three building blocks, the proof of concept of adaptivity with DDM is discussed.

conferences

2023

A Priori Verification Method for Curl-Conforming Vector Functions in Simplices

Adrian Amor-Martin, and Luis E. Garcia-Castillo

In 23rd International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE, 2023

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On the Validation of Curl-Conforming Higher-Order Basis Functions Using the Method of Manufactured Solutions

Adrian Amor-Martin, and Luis E. Garcia-Castillo

In 24th International Conference on Electromagnetics in Advanced Applications (ICEAA), 2023
Indirect Detection of Gravitational Waves Using an Analogue Electromagnetic Spacetime Modulated Medium

In 17th European Conference on Antennas and Propagation (EuCAP), 2023
Analogous Electromagnetic Wave Propagation in a Schwarzschild Black Hole Space-time Using Parallel Conducting Surfaces Waveguides

In 17th European Conference on Antennas and Propagation (EuCAP), 2023
Parallel Plates Waveguide-based Analogous Electromagnetic Model of the Gravitational Field of a Schwarzschild Black Hole

In Congreso Nacional de La URSI, 2023
Study of the Interaction Between Gravitational and Electromagnetic Waves through the Finite Differences Time Domain

In Congreso Nacional de La URSI, 2023
Predicción de Prestaciones de Un Resonador Por Técnicas de Inteligencia Artificial

Antonio Rueda-Escalona, Adrian Amor-Martin, and Jose A Belloch

In Congreso Nacional de La URSI, 2023
Sensor Activo de Alta Estabilidad y Sensibilidad Para Detección No Invasiva de Cáncer de Mama

Sandra Santiago-Mesas, Elizabeth Fernandez-Aranzamendi, Daniel Segovia-Vargas, and 1 more author

In Congreso Nacional de La URSI, 2023
A High-Stability and High-Sensitivity Active Sensor for Non-Invasive Breast Cancer Detection

Sandra Santiago-Mesas, Elizabeth Fernandez-Aranzamendi, Daniel Segovia-Vargas, and 2 more authors

In 53rd European Microwave Conference, 2023
Estudio de Técnicas de Inteligencia Artificial Para La Detección de Contaminantes

César Turienzo-Forcada, Adrian Amor-Martin, and Jose A Belloch

In Congreso Nacional de La URSI, 2023
Numerically Stable Implementation of Ewald Method for 1D Periodicity

Sergio Llorente-Romano, Luis E. Garcia-Castillo, and Adrian Amor-Martin

In , 2023
On the Use of the Method of Manufactured Solutions for the Domain Decomposition Method

Adrian Amor-Martin, and Luis E. Garcia-Castillo

In , 2023

2022

Analogous Maxwellian Algorithm for Photon Geodesic Calculation in General Static Isotropic Metrics

Enderson Falcón, Gabriel Santamaría-Botello, Adrián Amor, and 2 more authors

In 51st European Microwave Conference (EuMC), 2022
Diseño de Un Sensor Activo Para Monitorización No Invasiva

Sandra Santiago-Mesas, Daniel Segovia-Vargas, Adrian Amor-Martin, and 1 more author

In Congreso Nacional de La URSI, 2022
Diseño de Un Sensor Activo Para Monitorización No Invasiva

Sandra Santiago-Mesas, Daniel Segovia-Vargas, Adrian Amor-Martin, and 1 more author

In Congreso Nacional de La URSI, 2022
Experimental Insight into the Domain Decomposition Method for a Finite Element Method Code

Adrian Amor-Martin, and Luis E. Garcia-Castillo

In XIV Encuentro Ibérico de Electromagnetismo Computacional, 2022
Strategies to Parallelize a Finite Element Mesh Truncation Technique on Multi- and Manycore Architectures.

Jose Manuel Badia, Adrian Amor-Martin, Jose A Belloch, and 1 more author

In 22th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE, 2022
Convergence Study of H(Curl) Serendipity Basis Functions for Hexahedral Finite-Elements

Laszlo L. Toth, Adrian Amor-Martin, and Romanus Dyczij-Edlinger

In MIKON 2022, 2022

2021

3D Electromagnetic Modeling and Inversion Using an Open-Source Paradigm: Experiences and Perspectives

Octavio Castillo-Reyes, Pilar Queralt, Alex Marcuello, and 3 more authors

In SIAM Conference on Mathematical & Computational Issues in the Geosciences, 2021

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Electromagnetic modeling and inversion and High-performance Computing (HPC) have a fundamental role in solving the next generation of geoscience problems. These problems are complex, multidisciplinary, and require collaboration to understand and solve the physical equations, pre-process and post-process the associated data with physical experiments, and build interpretations from the analysis of the numerical results. In this talk, we present the value of integrating electromagnetic methods in applied geophysics, high-order finite element as the numerical method, and HPC as a computational platform to solve real-life test cases. As the main arguments of this talk, we present: 1) The advantages of developing and using open-source software in a multidisciplinary context; 2) Real cases of 3D electromagnetic modeling and inversion which exploits the computing capacity of the architecture. PETGEM (Parallel Edge-based Tool for Geophysical Electromagnetic Modelling, http://petgem.bsc.es) is used to compute the electromagnetic responses for each test case; 3) The importance of providing reproducible results that are easy to explore and even extend. This feature is essential to demonstrate that an open-source paradigm has the potential not only to reduce the time required to carry out research but also to disseminate results quickly. These points depict our experience and perspectives in the field of 3D electromagnetic modeling and inversion using an open-source paradigm.

2019

H(Curl)-Conforming Hierarchical Basis Functions on Prisms and Hexahedra

Adrian Amor-Martin, Laszlo L. Toth, and Romanus Dyczij-Edlinger

In Kleinheubacher Tagung 2019, 2019

Slides
Hierarchical H(Div) Basis Functions and Universal Matrices for Curvilinear Finite Elements

Laszlo L. Toth, Adrian Amor-Martin, and Romanus Dyczij-Edlinger

In Kinetics and BEM on the Saar, 2019

2018

Non-Conformal Domain Decomposition Method Supporting Hp-Discretizations

Adrian Amor-Martin, Daniel Garcia-Donoro, and Luis E. Garcia-Castillo

In XII Encuentro Ibérico de Electromagnetismo Computacional, 2018
Higher Order Finite Element Method Based on a Non-Conformal Domain Decomposition Method

Adrian Amor-Martin, Luis E. Garcia-Castillo, and Daniel Garcia-Donoro

In Emerging Trends in Applied Mathematics and Mechanics 2018, 2018
Towards a Scalable Hp Adaptive Finite Element Code Based on a Nonconformal Domain Decomposition Method

Adrian Amor-Martin, LE Garcia-Castillo, and D Garcia-Donoro

In 48th European Microwave Conference (EuMC), 2018

Slides
Non-Conformal Domain Decomposition Method Supporting Hp Discretizations

Adrian Amor-Martin, Daniel Garcia-Donoro, and Luis E. Garcia-Castillo

In International Workshop on Finite Elements for Microwave Engineering, 2018
Three-Level Parallelization of a Finite Element Code with Hybrid Meshes

Adrian Amor-Martin, Daniel Garcia-Donoro, and Luis E. Garcia-Castillo

In Congreso Nacional de la URSI, 2018

Slides
Acceleration of a Mesh Truncation Technique for a Finite Element Electromagnetics Code

Jose A Belloch, Adrian Amor-Martin, Daniel Garcia-Donoro, and 1 more author

In 18th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE, 2018
Recent Developments Regarding a Higher Order Finite Element Method Electromagnetic Simulator (HOFEM)

Daniel Garcia-Donoro, Adrian Amor-Martin, and Luis E. Garcia-Castillo

In XII Encuentro Ibérico de Electromagnetismo Computacional, 2018
Electromagnetic Finite Element Solver for HPC Environments Using Direct Substructuring Method

Daniel Garcia-Donoro, Wujie Mei, Adrian Amor-Martin, and 1 more author

In 48th European Microwave Conference (EuMC), 2018

2017

A Finite Element Mesh Truncation Technique for Scattering and Radiation Problems in HPC Environments

Adrian Amor-Martin, Daniel Garcia-Doñoro, and Luis E. Garcia-Castillo

In Computing and Electromagnetics International Workshop (CEM), 2017
Analysis of Dispersion Error of Higher-Order Curl-Conforming Prismatic Finite Element

Adrian Amor-Martin, Daniel Garcia-Donoro, and Luis E. Garcia-Castillo

In IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO), 2017

Slides
On the Design of Higher-Order Curl-Conforming Finite Elements and Its Assembly Features

Adrian Amor-Martin, Daniel Garcia-Donoro, and Luis E. Garcia-Castillo

In IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO), 2017

Slides
Higher-Order Finite Element Code for Electromagnetic Simularion on HPC Environments

Luis E. Garcia-Castillo, Daniel Garcia-Donoro, and Adrian Amor-Martin

In MUMPS User Days, 2017

Slides
Higher-Order Finite Element Electromagnetics Code for HPC Environments

Daniel Garcia-Donoro, Adrian Amor-Martin, and Luis E. Garcia-Castillo

In International Conference on Computational Science, ICCS, 2017

Slides
Algorithm for Simultaneous Adaptation and Time Step Iterations for the Electromagnetic Waves Propagation and Heating of the Human Head Induced by Cell Phone

Luis E. Garcia-Castillo, Ignacio Gomez-Revuelto, Adrian Amor-Martin, and 2 more authors

In International Conference on Computational Science, ICCS, 2017

2016

Posidonia: A Software Tool for HPC Scientific Simulations

Adrian Amor-Martin, Ignacio Martinez-Fernandez, and Luis E. Garcia-Castillo

In XI Encuentro Ibérico de Electromagnetismo Computacional, 2016
Comparison between Different Assembly Strategies for Higher-Order Curl-Conforming Prismatic Finite Elements

Adrian Amor-Martin, and Luis E. Garcia-Castillo

In XI Encuentro Ibérico de Electromagnetismo Computacional, 2016
Posidonia: A Tool for HPC and Remote Scientific Simulations

Adrian Amor-Martin, Ignacio Martinez-Fernandez, and Luis E. Garcia-Castillo

In FEM Workshop, 2016

Slides
Second-Order Nédélec Curl-Conforming Prism for Finite Element Computations

Adrian Amor-Martin, Daniel Garcia-Donoro, and Luis E. Garcia-Castillo

In FEM Workshop, 2016

Slides
HOFEM: Higher Order Finite Element Method Simulator for Antenna Analysis

Daniel Garcia-Donoro, Adrian Amor-Martin, Luis E. Garcia-Castillo, and 2 more authors

In IEEE Conference on Antenna Measurements & Applications (CAMA), 2016
Higher Order Finite Element Method Solver for the Analysis of Microwave Devices in Planar Technology

Daniel Garcia-Donoro, Sioweng Ting, Adrian Amor-Martin, and 2 more authors

In Microwave Conference (EuMC), 2016 46th European, 2016

2015

Implementation of the Second-Order Nédélec Curl-Conforming Prismatic Element for Computational Electromagnetics

Adrian Amor-Martin, Daniel Garcia-Donoro, and Luis E. Garcia-Castillo

In Congreso Nacional de la URSI, 2015

Slides

2014

State Estimation Using an Extended Kalman Filter with Privacy-Protected Observed Inputs

Francisco-Javier González-Serrano, Adrian Amor-Martin, and Jorge Casamayón-Antón

In IEEE International Workshop on Information Forensics and Security (WIFS), 2014

2013

Plataforma Web de Simulación Remota En Un Cluster de Computación Científica

Cristina Garcia-Muñoz, Adrian Amor-Martin, Ignacio Martinez-Fernandez, and 1 more author

In Congreso Nacional de la URSI, 2013

Slides

2012

Herramienta de Simulación Remota En Un Cluster de Computación Científica

Adrian Amor-Martin, Ignacio Martinez-Fernandez, and Luis E. Garcia-Castillo

In Congreso Nacional de la URSI, 2012

Slides

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