A testbench of arbitrary accuracy for electromagnetic simulations

Abstract

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.

CMMSE: A Priori Verification Method for Curl-Conforming Basis Functions in Simplices

“…Finally, a whole code using curl-conforming basis functions can be validated with analytical solutions in benchmark problems, e.g., rectangular cavities, [32]. However, minor mistakes in the basis functions might not affect the convergence rate of the solutions, especially with simplices where the convergence rates are close to (but not exactly) the order k since the mesh has a non-negligible effect, [37].…”

“…This orthogonalization, together with the difficulty of finding a procedure to provide with basis functions of arbitrary order might yield to basis functions which are not in the original Nédélec space provided in [2], or that span Nédélec-type spaces that satisfy the exactness property, [7]. Typically, the basis functions are directly validated using structures with an available analytical solution, e.g., [32], or verified with mathematical techniques as the method of manufactured solutions (MMS, [33], [34]). Both approaches require the full machinery of a FEM code and they are not the most efficient way to show that the spanned space of functions is correct.…”

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

“…This setup leads to a mesh with 80 elements and 640 unknowns. As a unit cell, we use a vacuum cube where a plane wave (21) impinges from (θ, φ) = ( π 2 , π 4 ). We use a 9 × 9 grid that allows us to test every different interface in Figure 3, and it is large enough to test the index generation algorithm from Section 2.2.3 as it uses all types of possible domains.…”

“…The outcome of the tests we should expect is that the introduction of the method is not worth it for small grids and it becomes more and more advantageous when the grid is larger. Without loss of generality, the problem that we solve is the propagation of a plane wave (expression (21)) whereas now we use 8324 tetrahedra and 53,124 unknowns for the unit cell. We use a personal workstation, equipped with a Linux distribution and with a six-core Intel Core i7-3970 and 32 GB of RAM, to obtain the results in this section.…”

“…As a result, we managed to increase the reliability of the code and shorten its development cycle compared to other software development plans. This process can be also applied in different codes, e.g., [20][21][22][23].…”