A finite-element capacitance matrix method for exterior Helmholtz problems

Numerische Mathematik

Volumn 75, Issue 2, 1996, Pages 175-204

  Ernst, Oliver G ^a  

^a TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030369255     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050236     Document Type: Article

References (23)

1. Bespalov, A., Kuznetsov, Y., Pironneau, O., Vallet, M. (1992): Fictitous domains with separable preconditioned versus unstructured adapted meshes. Tech. Report 1614, INRIA
2. Bjørstadt, P.E., Widlund, O.B. (1984): Solving elliptic problems on regions partitioned into substructures. Elliptic Problem Solvers II (Birkhoff G, Schoenstadt A, eds) pp. 245-255
3. Bjørstadt, P.E., Widlund, O.B. (1984): Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23 (1986), no. 6, 1097-1120
4. Börgers, C., Widlund, O.B. (1990): On finite element domain imbedding methods. SIAM J. Numer. Anal. 27 no. 4, 963-978
5. Bowman, J.J., Senior, T.B.A., Uslenghi, P.L.E. (1987): Electromagnetic and acoustic scattering by simple shapes. 2nd edn., Hemisphere Publishing Corporation
6. Buzbee, B., Golub, G., Nielson, C. (1970): On direct methods for solving Poisson's equation, SIAM J. Numer. Analysis 7, 627-656
7. Buzbee, B.L., Dorr, F.W., George, J.A., Golub, G.H. (1974): The direct solution of the discrete Poisson equation on irregular regions, SIAM J. Numer. Anal. 8, 722-736
8. Colton, D., Kress, R. (1983): Integral equation methods in scattering theory, Wiley, New York
9. Colton, D., Kress, R. (1983): Inverse acoustic and electromagnetic scattering theory (1992) Applied Mathematical Sciences, vol. 93, Springer-Verlag
10. Dryja, M. (1983): A finite-element capacitance matrix method for the elliptic problem. SIAM J. Numer. Anal. 20, 621
11. Ernst, O.G. (1994): Fast numerical solution of exterior Helmholtz problems with radiation boundary condition by imbedding. Ph.D. thesis, Stanford University
12. Freund, R.W., Nachtigal, N.M. (1992): Implementation details of the coupled QMR algorithm. Tech. Report 92, RIACS
13. Freund, R.W., Nachtigal, N.M. (1994): An implementation of the QMR method based on coupled two-term recurrences. SIAM J. Sci. Comput. 15, no. 2, 313-337
14. George, A. (1970): The use of direct methods for the solution of the discrete Poisson equation on non-rectangular regions, Tech. Report STAN-CS-70-159, Computer Science Dept., Stanford University, Stanford, CA
15. Hockney, W. (1970): POT4 - A fast direct Poisson-solver for the rectangle allowing some mixed boundary conditions and internal electrodes. Tech. report, IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, May 1979
16. Keller, J.B., Givoli, D. (1989): Exact non-reflecting boundary conditions. J. Comput. Phys. 82, 172-192
17. Kirsch, A. (1984): Generalized Boundary Value-and Control Problems for the Helmholtz Equation, Habilitation thesis, Göttingen
18. Kirsch, A. (1992): Remarks on some notions of weak solutions for the Helmholtz equation. Appl. Anal. 14, 7-24
19. Lebedev, N.N. (1972): Special functions and their applications, Dover
20. Masmoudi, M. (1987): Numerical solution for exterior problems, Numer. Math. 51, 87-101
21. Proskurowski, W., Widlund, O.B. (1976): On the numerical solution of Helmholtz's equation by the capacitance matrix method. Math. Comp. 30, 433-468
22. Swarztrauber, P.N. (1977): The methods of cyclic reduction, fourier analysis and the facr algorithm for the discrete solution of Poisson's equation on a rectangle. SIAM Rev. 19, 490-501
23. Widlund, O.B. (1984): Iterative methods for elliptic problems on regions partitioned into substructures. Proc. 6th Intern. Cont. Comput. Meth. Sci. Eng. (Glowinski R, Lions JL, eds.) Elsevier Science Publishers B.V., North Holland, pp. 33-45