The Time-Domain Lippmann-Schwinger Equation and Convolution Quadrature

被引：6

作者：

Lechleiter, Armin ^{[1
]}

Monk, Peter ^{[2
]}

机构：

[1] Univ Bremen, Ctr Ind Math, D-28359 Bremen, Germany

[2] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 31卷 / 02期

关键词：

convolution quadrature; Lippman-Schwinger; time domain; BOUNDARY INTEGRAL-EQUATIONS; NUMERICAL-SOLUTION; WAVE-EQUATION; DISCRETIZATION; SCATTERING; MULTISTEP;

D O I：

10.1002/num.21921

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider time-domain acoustic scattering from a penetrable medium with a variable sound speed. This problem can be reduced to solve a time-domain volume Lippmann-Schwinger integral equation. Using convolution quadrature in time and trigonometric collocation in space, we can compute an approximate solution. We prove that the time-domain Lippmann-Schwinger equation has a unique solution and prove conditional convergence and error estimates for the fully discrete solution for globally smooth sound speeds. Preliminary numerical results show that the method behaves well even for discontinuous sound speeds. (c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 517-540, 2015

引用

页码：517 / 540

页数：24

共 19 条

[1] Numerical solution of exterior Maxwell problems by Galerkin BEM and Runge-Kutta convolution quadrature [J].

Ballani, J. ;

Banjai, L. ;

Sauter, S. ;

Veit, A. .

NUMERISCHE MATHEMATIK, 2013, 123 (04) :643-670

[2]

BAMBERGER A., 1986, MATH METHOD APPL SCI, V8, P405, DOI [10.1002/mma.1670080127, DOI 10.1002/MMA.1670080127]

[3] RAPID SOLUTION OF THE WAVE EQUATION IN UNBOUNDED DOMAINS [J].

Banjai, L. ;

Sauter, S. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 47 (01) :227-249

[4]

Banjai L., 2014, STABLE NUMERICAL COU

[5] Runge-Kutta convolution quadrature for the Boundary Element Method [J].

Banjai, Lehel ;

Messner, Matthias ;

Schanz, Martin .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 245 :90-101

[6] Runge-Kutta convolution quadrature for operators arising in wave propagation [J].

Banjai, Lehel ;

Lubich, Christian ;

Melenk, Jens Markus .

NUMERISCHE MATHEMATIK, 2011, 119 (01) :1-20

[7] MULTISTEP AND MULTISTAGE CONVOLUTION QUADRATURE FOR THE WAVE EQUATION: ALGORITHMS AND EXPERIMENTS [J].

Banjai, Lehel .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (05) :2964-2994

[8] Analysis of Convolution Quadrature Applied to the Time-Domain Electric Field Integral Equation [J].

Chen, Q. ;

Monk, P. ;

Wang, X. ;

Weile, D. .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2012, 11 (02) :383-399

[9]

COLTON D., 2012, Inverse Acoustic and Electromagnetic Scattering Theory

[10]

Ha-Duong T, 2003, LECT NOTES COMP SCI, V31, P301

← 1 2 →