Test-Driven Development of a Substructuring Technique for the Analysis of Electromagnetic Finite Periodic Structures
Source abstract
Abstract
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.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Advanced Antenna and Metasurface Technologies · Antenna Design and Analysis · Microwave Engineering and Waveguides
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Signal Theory and Communications Department, University Carlos III of Madrid, Leganes, 28911 Madrid, Spain
References (35)
Show source-provided references
1. Jin, J.M. (2015). The Finite Element Method in Electromagnetics, John Wiley & Sons.
2. GetDDM: An Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic Wave Problems10.1016/j.cpc.2016.02.030 ↗
3. A Hybrid Conformal/Nonconformal Domain Decomposition Method for Multi-Region Electromagnetic Modeling10.1109/TAP.2014.2300149 ↗
4. Nonconformal Domain Decomposition Methods for Solving Large Multiscale Electromagnetic Scattering Problems10.1109/JPROC.2012.2217931 ↗
5. Multi-parameter polynomial order reduction of linear finite element models10.1080/13873950701844220 ↗
6. A Compact Basis for Reliable Fast Frequency Sweep via the Reduced-Basis Method10.1109/TMTT.2018.2865957 ↗
7. Zhu, Y., and Cangellaris, A.C. (2006). Multigrid Finite Element Methods for Electromagnetic Field Modeling, John Wiley & Sons.10.1002/0471786381 ↗
8. Algorithmic Enhancements, Model-Order Reduction, and Multigrid Aspects in Contemporary Finite Element Implementations10.1109/TMAG.2009.2012592 ↗
9. Paszynski, M., Pardo, D., Torres-Verdın, C., Demkowicz, L., and Calo, V. (2007). A Multi Level Direct Sub-Structuring Multi-Frontal Parallel Solver for the hp-Finite Element Method, ICES-Report; The University of Texas at Austin.
10. Mesh-based multi-frontal solver with reuse of partial LU factorizations for antenna array10.1016/j.jocs.2016.10.008 ↗
11. A frequency selective surface with miniaturized elements10.1109/TAP.2007.895567 ↗
12. Mailloux, R.J. (2017). Phased Array Antenna Handbook, Artech House.
13. Perspectives on EM metamaterials10.1016/S1369-7021(09)70071-9 ↗
14. Yang, F., and Rahmat-Samii, Y. (2009). Electromagnetic Band Gap Structures in Antenna Engineering, Cambridge University Press.10.1017/CBO9780511754531 ↗
15. Finite element analysis of periodic structures without constrained meshes10.1109/TAP.2008.928776 ↗
16. A Nonstandard Schwarz Domain Decomposition Method for Finite-Element Mesh Truncation of Infinite Arrays10.1109/TAP.2018.2866532 ↗
17. Garcia-Donoro, D., Amor-Martin, A., Garcia-Castillo, L.E., Salazar-Palma, M., and Sarkar, T.K. (2016, January 23–27). HOFEM: Higher Order Finite Element Method Simulator for Antenna Analysis. Proceedings of the 2016 IEEE Conference on Antenna Measurements & Applications (CAMA), Syracuse, NY, USA.10.1109/CAMA.2016.7815776 ↗
18. Marchand, R., and Davidson, D.B. The Method of Manufactured Solutions in 3D for the verification of Computational Electromagnetics. Proceedings of the 2012 IEEE International Symposium on Antennas and Propagation, Chicago, IL, USA.10.1109/APS.2012.6348008 ↗
19. Verification Process of Finite-Element Method Code for Electromagnetics: Using the method of manufactured solutions10.1109/MAP.2016.2520308 ↗
20. On local and global species conservation errors for nonlinear ecological models and chemical reacting flows
21. A testbench of arbitrary accuracy for electromagnetic simulations
22. Forward modelling of geophysical electromagnetic data on unstructured grids using an adaptive mimetic finite-difference method10.1007/s10596-021-10042-5 ↗
23. A finite-element framework for a mimetic finite-difference discretization of Maxwell’s equations10.1137/20M1382568 ↗
24. Monk, P. (2003). Finite Element Methods for Maxwell’s Equations, Oxford University Press.10.1093/acprof:oso/9780198508885.001.0001 ↗
25. Dooley, J. (2017). Software Development, Design and Coding: With Patterns, Debugging, Unit Testing, and Refactoring, Apress.
26. Rilee, M., and Clune, T. (2014, January 21). Towards Test Driven Development for Computational Science with pFUnit. Proceedings of the 2014 Second International Workshop on Software Engineering for High Performance Computing in Computational Science and Engineering, New Orleans, LA, USA.10.1109/SE-HPCCSE.2014.5 ↗
27. Beck (2002). Test Driven Development: By Example, Addison-Wesley Longman Publishing Co., Inc.
28. Clune, T. (2012). Test Driven Development of Scientific Models, Technical Report; Software Systems Support Office Earth Science Division NASA Goddard Space Flight Center.
29. Clune, T., and Womack, B. (2021, October 21). pFUnit Web Page. Available online: https://github.com/Goddard-Fortran-Ecosystem/pFUnit.
30. Software Testing and Verification in Climate Model Development10.1109/MS.2011.117 ↗
31. Higher-Order Finite Element Electromagnetics Code for HPC Environments10.1016/j.procs.2017.05.239 ↗
32. Melendo, A., Coll, A., Pasenau, M., Escolano, E., and Monros, A. (2021, October 21). GiD Home. Available online: www.gidhome.com.
33. Second-Order Nédélec Tetrahedral Element for Computational Electromagnetics10.1002/(SICI)1099-1204(200003/06)13:2/3<261::AID-JNM360>3.0.CO;2-L ↗
34. Salazar-Palma, M., Sarkar, T.K., García-Castillo, L.E., Roy, T., and Djordjevic, A.R. (1998). Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling, Artech House Publishers, Inc.
35. Balanis, C.A. (1989). Advanced Engineering Electromagnetics, John Wiley & Sons.