FAST WAVELET-BASED ALGORITHMS FOR LINEAR EVOLUTION-EQUATIONS

被引:30
作者
ENGQUIST, B
OSHER, S
ZHONG, SF
机构
关键词
WAVELETS; HYPERBOLIC; PARABOLIC; NUMERICAL METHODS;
D O I
10.1137/0915048
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The authors devise a class of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin [Comm. Pure Appl. Math., 44 (1991), pp. 141-1841, which they applied to general Calderon-Zygmund type integral operators. The authors apply a modification of their idea to linear hyperbolic and parabolic equations, with spatially varying coefficients. The complexity for hyperbolic equations in one dimension is reduced from O(N2) to O(N log3 N). There are somewhat better gains for parabolic equations in multidimensions.
引用
收藏
页码:755 / 775
页数:21
相关论文
共 9 条
[1]   FAST WAVELET TRANSFORMS AND NUMERICAL ALGORITHMS .1. [J].
BEYLKIN, G ;
COIFMAN, R ;
ROKHLIN, V .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (02) :141-183
[2]   ORTHONORMAL BASES OF COMPACTLY SUPPORTED WAVELETS [J].
DAUBECHIES, I .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (07) :909-996
[3]   A FAST ALGORITHM FOR THE EVALUATION OF HEAT POTENTIALS [J].
GREENGARD, L ;
STRAIN, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1990, 43 (08) :949-963
[4]   THE FAST GAUSS TRANSFORM [J].
GREENGARD, L ;
STRAIN, J .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1991, 12 (01) :79-94
[5]   RATE OF CONVERGENCE OF SOME DIFFERENCE SCHEMES [J].
HEDSTROM, GW .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1968, 5 (02) :363-&
[6]   THE OPTIMAL ACCURACY OF DIFFERENCE-SCHEMES [J].
ISERLES, A ;
STRANG, G .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 277 (02) :779-803
[7]  
MADAY Y, IN PRESS CR ACAD SCI
[8]  
Richtmyer RD., 1967, DIFFERENCE METHODS I
[9]   RAPID SOLUTION OF INTEGRAL-EQUATIONS OF CLASSICAL POTENTIAL-THEORY [J].
ROKHLIN, V .
JOURNAL OF COMPUTATIONAL PHYSICS, 1985, 60 (02) :187-207