Sparsity of Runge–Kutta convolution weights for the three-dimensional wave equation

被引：0
作者：
Lehel Banjai
Maryna Kachanovska
机构：
[1] Heriot-Watt University,School of Mathematical & Computer Sciences
[2] Max Planck Institute for Mathematics in the Sciences,undefined
来源：
BIT Numerical Mathematics | 2014年 / 54卷
关键词：
Convolution quadrature; Runge–Kutta methods; Time-domain boundary integral equations; Wave equation; 65R20; 65L06; 35L05; 65M38;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Wave propagation problems in unbounded homogeneous domains can be formulated as time-domain integral equations. An effective way to discretize such equations in time are Runge–Kutta based convolution quadratures. In this paper the behaviour of the weights of such quadratures is investigated. In particular approximate sparseness of their Galerkin discretization is analyzed. Further, it is demonstrated how these results can be used to construct and analyze the complexity of fast algorithms for the assembly of the fully discrete systems.
引用
收藏
页码：901 / 936
页数：35
相关论文
共 35 条
[1]  
Alexander R(1977)Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E’.s SIAM J. Numer. Anal. 14 1006-1021
[2]  
Ambroladze A(1999)Rational interpolants with preassigned poles, theoretical aspects Stud. Math. 132 1-14
[3]  
Wallin H(1986)Formulation variationnelle espace-temps pour le calcul par potentiel retardé de la diffraction d’une onde acoustique Math. Methods Appl. Sci. 8 405-435
[4]  
Bamberger A(1986)Formulation variationnelle pour le calcul de la diffraction d’une onde acoustique par une surface rigide Math. Methods Appl. Sci. 8 598-608
[5]  
Ha-Duong T(2010)Multistep and multistage convolution quadrature for the wave equation: algorithms and experiments SIAM J. Sci. Comput. 32 2964-2994
[6]  
Bamberger A(2011)An error analysis of Runge–Kutta convolution quadrature BIT Numer. Math. 51 483-496
[7]  
Ha-Duong T(2011)Runge–Kutta convolution quadrature for operators arising in wave propagation Numer. Math. 119 1-20
[8]  
Banjai L(2004)Stability and convergence of collocation schemes for retarded potential integral equations SIAM J. Numer. Anal. 42 1167-1188
[9]  
Banjai L(1973)-stable methods and Padé approximations to the exponential SIAM J. Math. Anal. 4 671-680
[10]  
Lubich C(1999)The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena IEEE Antennas Propag. Mag. 41 39-52
1234