A fast and accurate algorithm for a Galerkin boundary integral method

Computational Mechanics

Volumn 37, Issue 1, 2005, Pages 96-109

  Wang, J ^a   Crouch, S L ^b   Mogilevskaya, S G ^b  

^a UNIVERSITY OF FLORIDA   (United States)

^b University of Minnesota   (United States)

Author keywords

Asymptotic expansion; Circular inhomogeneity; Fast multipole algorithm; Galerkin boundary integral method; Orthogonal function; Straight crack; Taylor series expansion; Tree data structure

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY ELEMENT METHOD; COMPUTATIONAL METHODS; DATA STRUCTURES; ELECTROSTATICS; GALERKIN METHODS; PROBLEM SOLVING;

ASYMPTOTIC EXPANSION; CIRCULAR INHOMOGENEITY; FAST MULTIPOLE ALGORITHM; GALERKIN BOUNDARY INTEGRAL METHOD; ORTHOGONAL FUNCTION; STRAIGHT CRACK; TAYLOR SERIES EXPANSION; TREE DATA STRUCTURE;

ALGORITHMS;

EID: 27244452869     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-005-0702-5     Document Type: Conference Paper

References (25)

1. Barnes RJ, Janković I (1999) Two-dimensional flow through large number of circular inhomogeneities. J. Hydrology 226:204-210
2. Carrier J, Greengard L, Rokhlin V (1988) A fast adaptive multipole algorithm for particle simulations. SIAM J Sci Stat Comput 9:669-686
3. Cheng H, Greengard L, Rokhlin V (1999) A fast adaptive multipole algorithm in three dimensions. J Comput Phys 155:468-498
4. Englund J, Helsing J (2003) Stress computations on perforated polygonal domains. Eng Anal Bound Elem 27:533-546
5. Fu Y, Klimkowski KJ, Rodin GJ, Berger E, Browne JC, Singer JK, Van De Geijn RA, Vemaganti KS (1998) A fast solution method for three-dimensional many-particle problems of linear elasticity. Int J Numer Meth Engrg 42:1215-1229
6. Golub GH, Van Loan CF (1996) Matrix Computations (3rd edit). John Hopkins University: Baltimore
7. Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys 73:325-348
8. Helsing J, Peters G (1999) Integral equation methods and numerical solutions of crack and inclusion problems in planar elastostatics. SIAM J Appl Math 59:965-982
9. Jonsson A (2002) Integral equation methods for fracture mechanics and micro-mechanics problems. PhD Thesis, Royal Institute of Technology, Sweden
10. Linkov AM (1983) Plane problems of the static loading of a piecewise homogeneous linearly elastic medium. J Appl Math Mech 47:527-532
11. Linkov AM, Mogilevskaya SG (1998) Complex hypersingular BEM in plane elasticity problems. In: Sladek V, Sladek J (eds) Singular Integrals in Boundary Element Methods (Chapter 9), Computational Mechanics Publications: Southhampton
12. Mogilevskaya SG, Crouch SL (2001) A Galerkin boundary integral method for multiple circular elastic inclusions. Int J Numer Meth Engrg 52:1069-1106
13. Mogilevskaya SG, Crouch SL (2004) A Galerkin boundary integral method for multiple circular elastic inclusions with uniform interphase layers. Int J Solids Struct 41:1285-1311
14. Muskhelishvili NI (1963) Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff: Groningen
15. Nishimura N, Yoshida K, Kobayashi S (1999) A fast multipole boundary integral equation method for crack problems in 3D. Eng Anal Bound Elem 23:97-105
16. Peirce AP, Napier JAL (1995) A spectral multipole method for efficient solution of large-scale boundary element methods in elastostatics. Int J Numer Meth Engrg 38:4009-4034
17. Popov V, Power H (2001) An O(N) Taylor series multipole boundary element method for three-dimensional elasticity problems. Eng Anal Bound Elem 25:7-18
18. Rokhlin V (1985) Rapid solution of integral equations of classical potential theory. J Comput Phys 60:187-207
19. Strack ODL, Janković I, Barnes R (1999) The Superblock approach for the analytic element method. J Hydrology 226:179-187
20. Wang J, Mogilevskaya SG, Crouch SL (2001) A Galerkin boundary integral method for nonhomogeneous materials with cracks. In: Elsworth D, Tinucci J, Heasley K (eds) Rock Mechanics in the National Interest, AA Balkema: Lisse pp. 1453-1460
21. Wang J, Crouch SL, Mogilevskaya SG (2003a) A complex boundary integral method for multiple circular holes in an infinite plane. Eng Anal Bound Elem 27:789-802
22. Wang J, Mogilevskaya SG, Crouch SL (2003b) A numerical procedure for multiple circular holes and elastic inclusions in a finite domain with a circular boundary. Comput Mech 32:250-258
23. Wang J (2004) Numerical modeling of elastic materials with inclusions, holes, and cracks. PhD Thesis, University of Minnesota
24. Wang J, Mogilevskaya SG, Crouch SL (2005) An embedding method for modeling micromechanical behavior and macroscopic properties of fiber-reinforced composites. Int J Solids Struct 42:4588-4612
25. Ying L, Biros G, Zorin D (2004) A kernel-independent adaptive fast multipole algorithm in two and three dimensions. J Comp Phys 196:591-626