An FMM for periodic boundary value problems for cracks for Helmholtz' equation in 2D

International Journal for Numerical Methods in Engineering

Volumn 73, Issue 3, 2008, Pages 381-406

  Otani, Yoshihiro ^a   Nishimura, Naoshi ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

BIEM; FMM; Helmholtz' equation; Periodic problems; Stopband

Indexed keywords

CRACK PROPAGATION; FOURIER ANALYSIS; HELMHOLTZ EQUATION; NUMERICAL METHODS; TWO DIMENSIONAL;

ENERGY TRANSMITTANCE; FAST MULTIPLE METHOD;

BOUNDARY VALUE PROBLEMS;

BOUNDARY VALUE PROBLEMS; CRACK PROPAGATION; FOURIER ANALYSIS; HELMHOLTZ EQUATION; NUMERICAL METHODS; TWO DIMENSIONAL;

EID: 38349142197     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2077     Document Type: Article

References (14)

1. Greengard L, Rokhlin V. A fast algorithm for particle simulations. Journal of Computational Physics 1987; 73:325-348.
2. Nishimura N. Fast multipole accelerated boundary integral equation methods. Applied Mechanics Reviews 2002; 55: 299-324.
3. Houzaki K, Nishimura N, Otani Y An FMM for periodic rigid-inclusion problems and its application to homogenisation. In Inverse Problems, Multi-Scale Analysis and Effective Medium Theory, Contemporary Mathematics, vol. 408, Ammari H, Kang H (eds). AMS: Providence, RI, 2006; 81-98.
4. Otani Y, Nishimura N. A fast multipole boundary integral equation method for periodic boundary value problems in three-dimensional elastostatics and its application to homogenisation. International Journal for Multiscale Computational Engineering 2006; 4(4):487-500.
5. Greengard L, Helsing J. On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites. Journal of the Mechanics and Physics of Solids 1998; 46:1441-1462.
6. Rodin GJ, Overfelt JR. Periodic conduction problems: the fast multipole method and convergence of integral equations and lattice sums. Proceedings of the Royal Society of London, Series A 2004; 460:2883-2902.
7. Sangani AS, Mo G. An O(N) algorithm for Stokes and Laplace interactions of particles. Physics of Fluids 1996; 8: 1990-2010.
8. Zinchenko AZ, Davis RH. An efficient algorithm for hydrodynamical interaction of many deformable drops. Journal of Computational Physics 2000; 157: 539-587.
9. Greengard L, Kropinski MC. Integral equation methods for Stokes flow in doubly-periodic domains. Journal of Engineering Mathematics 2004; 48: 157-170.
10. Joannopoulos JD, Meade RD, Winn JN. Photonic Crystals. Princeton University Press: Princeton, NJ, 1995.
11. Ewald PP. Die Berechnung Optischer und Electrostatischer Gitterpotentiale. Annalen der Physik 1921; 64: 253-287.
12. Rokhlin V. Rapid solution of integral equations of scattering theory in two dimensions. Journal of Computational Physics 1990; 86:414-439.
13. Achenbach JD, Li ZL. Reflection and transmission of scalar waves by a periodic array of screens. Wave Motion 1986; 8: 225-234.
14. Linton CM, McIver P. Handbook of Mathematical Techniques for Wave/ Structure Interactions. Chapman & Hall/CRC: London, Boca Raton, FL, 2001.