Shape derivatives for scattering problems

Hiptmair, Ralf1; Li, Jingzhi2

2018-10

10.1088/1361-6420/aad34a

INVERSE PROBLEMS   影响因子和分区

0266-5611

1361-6420

In this paper we study shape derivatives of solutions of acoustic and electromagnetic scattering problems in frequency domain from the perspective of differential forms following Hiptmair and Li's work (2013 Ann. Mat. Pura Appl. 192 1077-98). Relying on variational formulations, we present a unified framework for the derivation of strong and weak forms of derivatives with respect to variations of the shape of an impenetrable (resp. penetrable) scatterer, when we impose Dirichlet, Neumann, or impedance (resp. transmission) conditions on its boundary (resp. interface). In 3D for degrees l = 0 and l = 1 of the forms we obtain known and new formulas for shape derivatives of solutions of Helmholtz and Maxwell equations. They can form the foundation for numerical approximation with finite elements or boundary elements.

shape derivative shape calculus differential forms acoustic scattering electromagnetic scattering

SCI ; EI

英语

通讯

Shenzhen Sci-Tech Fund[JCYJ20160530184212170] ; Shenzhen Sci-Tech Fund[JCYJ20170818153840322]

Mathematics ; Physics

Mathematics, Applied ; Physics, Mathematical

WOS:000440549800001

IOP PUBLISHING LTD

20183605768283

Acoustic impedance ; Calculations ; Differentiation (calculus) ; Frequency domain analysis ; Maxwell equations

Acoustic Waves:751.1 ; Acoustic Properties of Materials:751.2 ; Mathematics:921

PHYSICS

Web of Science

1.Swiss Fed Inst Technol, Seminar Appl Math, D MATH, CH-8092 Zurich, Switzerland
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

Hiptmair, Ralf,Li, Jingzhi. Shape derivatives for scattering problems[J]. INVERSE PROBLEMS,2018,34(10).

Hiptmair, Ralf,&Li, Jingzhi.(2018).Shape derivatives for scattering problems.INVERSE PROBLEMS,34(10).

Hiptmair, Ralf,et al."Shape derivatives for scattering problems".INVERSE PROBLEMS 34.10(2018).