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

Amor-Martín, Adrián; Garcı́a-Castillo, L.E.; Tóth, Lászlo Levente; Floch, O.; Dyczij‐Edlinger, Romanus

doi:10.1109/tap.2023.3294001

Cited by 1 publication

(3 citation statements)

References 52 publications

(83 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another popular verification method is the Method of Manufactured Solutions, employed in [33], [34], [36]. The method of manufactured solutions consists of manufacturing an analytical solution to some differential equation by solving the problem backward.…”

Section: Verification Of Curl-conforming Basis Functionsmentioning

confidence: 99%

“…The method of manufactured solutions consists of manufacturing an analytical solution to some differential equation by solving the problem backward. If this analytical solution is a polynomial inside R k , the error between the analytical solution and the solution provided by an FEM code is numerically zero, [34].…”

Section: Verification Of Curl-conforming Basis Functionsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Amor-Martin,

Garcia-Castillo

2023

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Verification Of Curl-conforming Basis Functionsmentioning

confidence: 99%

Section: Verification Of Curl-conforming Basis Functionsmentioning

confidence: 99%