An efficient vector finite element method for nonlinear electromagnetic modeling

DOI10.1016/j.jcp.2007.01.031zbMath1129.78019OpenAlexW2031518244MaRDI QIDQ2381210

Yanyan Li

Publication date: 14 September 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://digital.library.unt.edu/ark:/67531/metadc897483/

zbMATH Keywords

finite element methodMaxwell's equationsnonlinear optics

Mathematics Subject Classification ID

Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Antennas, waveguides in optics and electromagnetic theory (78A50) Lasers, masers, optical bistability, nonlinear optics (78A60)

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Uses Software

• FEMSTER

Cites Work

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• Mixed finite elements in \(\mathbb{R}^3\)
• A finite element method for approximating the time-harmonic Maxwell equations
• A high order mixed vector finite element method for solving the time dependent Maxwell equations on unstructured grids
• An analysis of Nédélec's method for the spatial discretization of Maxwell's equations
• A Vector Finite Element Time-Domain Method for Solving Maxwell's Equations on Unstructured Hexahedral Grids
• Canonical construction of finite elements
• Finite Element Methods for Maxwell's Equations
• Stable Finite Elements for Problems with Wild Coefficients
• Dispersive properties of high–order Nédélec/edge element approximation of the time–harmonic Maxwell equations
• High-Order Symplectic Integration Methods for Finite Element Solutions to Time Dependent Maxwell Equations
• A generalized mass lumping technique for vector finite-element solutions of the time-dependent Maxwell equations