Spectral domain embedding for elliptic PDEs in complex domains

Journal of Computational and Applied Mathematics

Volumn 225, Issue 2, 2009, Pages 541-557

  Lui, S H ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Domain embedding; Fictitious domain; Irregular domain; Pseudospectral method; Spectral collocation; Spectral method

Indexed keywords

AIRCRAFT ENGINES; BOUNDARY CONDITIONS; FLOW OF FLUIDS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SPECTRUM ANALYSIS;

DOMAIN EMBEDDING; FICTITIOUS DOMAIN; IRREGULAR DOMAIN; PSEUDOSPECTRAL METHOD; SPECTRAL COLLOCATION; SPECTRAL METHOD;

DOMAIN DECOMPOSITION METHODS;

EID: 58849135272     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.08.034     Document Type: Article

References (30)

1. Atamian C., Dinh Q.V., Glowinski R., He J., and Periaux J. Control approach to fictitious domain methods: Applications to fluid dynamics and electromagnetics. In: Glowinski R., Kuznetsov Yu.A., Meurant G.A., Periaux J., and Widlund O.B. (Eds). Proc. Fourth Int. Conf. on Domain Decomposition Methods for Partial Differential Equations (1991), SIAM, Philadelphia 275-309
2. Badea L., and Daripa P. On a boundary control approach to domain embedding methods. SIAM J. Control Optim. 40 (2001) 421-449
3. Badea L., and Daripa P. On a Fourier method for embedding domains using an optimal distributed control. Numer. Algorithms 32 (2003) 261-273
4. Badea L., and Daripa P. A domain embedding method using optimal distributed control and a fast algorithm. Numer. Algorithms 36 (2004) 95-112
5. Bernardi C., and Maday Y. Spectral Methods. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis vol. 5 (1997), Amsterdam, North-Holland
6. Borgers C., and Widlund O.B. On finite element domain imbedding methods. SIAM J. Numer. Anal. 27 (1990) 963-978
7. Boyd J.P. Chebyshev and Fourier Spectral Methods. 2nd rev. edition (2001), Dover, Mineola, New York
8. Bueno-Orovio A., Perez-Garcia V.M., and Fenton F.H. Spectral methods for partial differential equations in irregular domains: The spectral smoothed boundary method. SIAM J. Sci. Comput. 28 (2006) 886-900
9. Buzbee B.L., Dorr F.W., George J.A., and Golub G.H. The direct solution of the discrete Poisson equation on irregular regions. SIAM J. Numer. Anal. 8 (1971) 722-736
10. Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. Spectral Methods-Fundamentals in Single Domains (2006), Springer-Verlag, New York
11. Deville M.O., Fischer P.F., and Mund E.H. High-Order Methods for Incompressible Fluid Flow (2002), Cambridge University Press, Cambridge
12. Dryja M. A finite element capacitance matrix method for the elliptic problem. SIAM J. Numer. Anal. 20 (1983) 671-680
13. Elghaoui M., and Pasquetti R. A spectral embedding method applied to the advection-diffusion equation. J. Comput. Phys. 125 (1996) 464-476
14. Elghaoui M., and Pasquetti R. Mixed spectral-boundary element embedding algorithms for the Navier-Stokes equations in the vorticity-stream function formulation. J. Comput. Phys. 153 (1999) 82-100
15. Fornberg B. A Practical Guide to Pseudospectral Methods (1996), Cambridge University Press, Cambridge
16. Funaro D. Spectral Elements for Transport-Dominated Equations (1997), Springer-Verlag, Berlin, Heidelberg
17. Glowinski R., Pan T.-W., and Periaux J. A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 112 (1994) 133-148
18. Gottlieb D., and Orszag S.A. Numerical Analysis of Spectral Methods (1977), SIAM, Philadelphia
19. Guo B.Y. Spectral Methods and Their Applications (1998), World Scientific, Singapore
20. Hesthaven J., Gottlieb S., and Gottlieb D. Spectral Methods for Time-Dependent Problems (2007), Cambridge University Press, Philadelphia
21. Karniadakis G., and Sherwin S. Spectral/hp Element Methods for Computational Fluid Dynamics. 2nd edition (2005), Oxford University Press, Oxford
22. Korczak K.Z., and Patera A.T. An isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry. J. Comput. Phys. 62 (1986) 361-382
23. Marchuk G.I., Kuznetsov Yu.A., and Matsokin A.M. Fictitious domain and domain decomposition methods. Soviet J. Numer. Anal. Math. Modelling 1 (1986) 3-35
24. Mayo A. The fast solution of Poisson's and the biharmonic equations on irregular regions. SIAM J. Numer. Anal. 21 (1984) 285-299
25. Orszag S.A. Spectral methods for problems in complex geometries. J. Comput. Phys. 37 (1980) 70-92
26. Proskurowski W., and Vassilevski P.S. Preconditioning capacitance matrix problems in domain imbedding. SIAM J. Sci. Comput. 15 (1994) 77-88
27. Quarteroni A., and Valli A. Numerical Approximation of Partial Differential Equations (1994), Springer-Verlag, Berlin, Heidelberg
28. Quarteroni A., and Valli A. Domain Decomposition Methods for Partial Differential Equations (1999), Oxford University Press, Oxford
29. Toselli A., and Widlund O. Domain Decomposition Methods-Algorithms and Theory (2005), Springer-Verlag, Berlin
30. Trefethen L.N. Spectral Methods in Matlab (2000), SIAM, Philadelphia