A Refinement-by-Superposition hp-Method for H(curl)- and H(div)-Conforming Discretizations

被引：1

作者：

Harmon, Jake J. ^{[1
,2
]}

Corrado, Jeremiah ^{[1
,3
]}

Notaros, Branislav M. ^{[1
]}

机构：

[1] Colorado State Univ, Dept Elect & Comp Engn, Ft Collins, CO 80523 USA

[2] Los Alamos Natl Lab, Theoret Div, Appl Math & Plasma Phys Grp, Los Alamos, NM 87545 USA

[3] Hewlett Packard Enterprise, Chapel Language Team, Seattle, WA 98101 USA

来源：

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION | 2023年 / 71卷 / 12期

关键词：

Computational electromagnetics (CEMs); continuous Galerkin; finite element method (FEM); higher order methods; hp-refinement; refinement-by-superposition (RBS); FINITE-ELEMENT METHOD; P-VERSION; DISCRETE COMPACTNESS; ADAPTIVITY; 1-DIMENSION; CONVERGENCE; ELECTROMAGNETICS; H(DIV);

D O I：

10.1109/TAP.2023.3331574

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

We present refinement-by-superposition (RBS) hp-refinement infrastructure for computational electromagnetics (CEMs), which permits exponential rates of convergence. In contrast to dominant approaches to hp-refinement for continuous Galerkin methods, which rely on explicit constraint equations, the multilevel strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease, and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS hp-method for refinement with H (curl)- and H (div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS hp-refinement. As an additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.

引用

页码：9357 / 9364

页数：8

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