Far East Journal of Applied Mathematics

The Far East Journal of Applied Mathematics publishes original research papers and survey articles in applied mathematics, covering topics such as nonlinear dynamics, approximation theory, and mathematical modeling. It encourages papers focusing on algorithm development.

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FINITE ELEMENT SOLUTION OF A RADIATION/PROPAGATION PROBLEM FOR A HELMHOLTZ EQUATION WITH A COMPACTLY SUPPORTED NONLINEARITY

Authors

  • Lutz Angermann

Keywords:

Scattering, radiation, nonlinear Helmholtz equation, nonlinearly polarizable medium, DtN operator, truncation, finite element method

DOI:

https://doi.org/10.17654/0972096023016

Abstract

A finite element method for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model consists of a nonlinear Helmholtz equation that is reduced to a spherical domain.

The (exemplary) finite element method is formed by Courant-type elements with curved facets at the boundary of the spherical computational domain. This method is examined for its well-posedness, in particular the validity of a discrete inf-sup condition of the modified sesquilinear form uniformly with respect to both the truncation and the mesh parameters is shown. Under suitable assumptions to the nonlinearities, a quasi-optimal error estimate is obtained. Finally, the satisfiability of the approximation property of the finite element space required for the solvability of a class of adjoint linear problems is discussed.

Received: July 22, 2023
Accepted: September 14, 2023

References

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Published

2023-12-13

Issue

Vol. 116 No. 4 (2023)

Section

Articles

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How to Cite

FINITE ELEMENT SOLUTION OF A RADIATION/PROPAGATION PROBLEM FOR A HELMHOLTZ EQUATION WITH A COMPACTLY SUPPORTED NONLINEARITY. (2023). Far East Journal of Applied Mathematics, 116(4), 311-356. https://doi.org/10.17654/0972096023016

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