Numerical Solution of Helmholtz's Equation by Implicit Capacitance Matrix Methods

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Numerical Solution of Helmholtz's Equation by Implicit Capacitance Matrix Methods

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 5 , Issue 1 (March 1979) table of contents

Pages: 36 - 49

Year of Publication: 1979

ISSN:0098-3500

Author

Wlodzimierz Proskurowski

Department of Mathematics, University of Southern California, Los Angeles, CA

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 16, Downloads (12 Months): 84, Citation Count: 3

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BANEGAS, A Fast Potsson solvers for problems with sparsity. Math. Comp. 32 (1978), 441-446.
	2	BUZBEE, B. L, AND DORR, F. W The dtrect solution of the blharmomc equation on rectangular regions and the Polsson equation on irregular regions. SIAM J. Nurner Anal. 11 (1974), 753-763.
	3	Coscus, P, GOLUB, G H., Arid O'LEARY, D P. A generalized conjugate gradmnt method for the solution of elhptic partial differential equations. In Proc Symp. on Sparse Matrix Computation, J R. Bunch and D.J Rose, Eds, Academm Press, New York, 1976.
	4	John A George, The use of direct methods for the solution of the discrete Poisson equation on non-rectangular regions, Stanford University, Stanford, CA, 1970
	5	HAYES, R M. Iterat~ve methods of solving hnear problems in Hflbert space, contributions to the solution of systems of hnear equations and the determination of elgenvalues, 0 Taussky, Ed., Nat. Bur Stand. (Appl. Math. Set. 39), pp. 71-103, 1954
	6	LEARY, D P, AND WIDLUND, O ERDA-NYU Rep. To appear.
	7	PROSKUROWSKI, W Four Fortran programs for numerically solving Helmholtz's equation m an arbitrary bounded planar region Rep. 7516, Lawrence Berkeley Lab., Berkeley, Calif., 1978.
	8	PROSKUROWSKI, W. On the numerical solution of the elgenvalue problem of the Laplace operator by a capacitance matrix method. Computing 20 (1978), 139-151
	9	PROSKUROWSKI, W., AND WIDLUND, O On the numerical soluhon of Helmholtz's equation by the capacitance matrix method. Math. Comp. 30 (1976), 433-468.
	10	Sm~.n, A. Fast Poisson solver on nonrectangular domains. New York U., Ph.D. Thesis, June 1976.
	11	WIDLUND, O. Oil the use of fast methods for separable fimte difference equations for the solution of general elliptic problems. In Sparse Matrices and Thew Apphcatmns, D.J. Rose and R A Willoughby, Eds, Plenum Press, New York, 1972
	12	WIDLUND, O. Capacitance matrLx methods for Helmholtz's equation on general bounded regions. mIn Proc. Meeting m Oberwolfach, Lecture Notes in Mathematics, vol. 631, Springer-Verlag, New York, 1978, 209-219.

CITED BY 3

	Dianne P. O'Leary , Olof Widlund, Algorithm 572: Solution of the Helmholtz Equation for the Dirichlet Problem on General Bounded Three-Dimensional Regions [D3], ACM Transactions on Mathematical Software (TOMS), v.7 n.2, p.239-246, June 1981
	Wlodzimierz Proskurowski, Algorithm 593: A Package for the Helmholtz Equation in Nonrectangular Planar Regions, ACM Transactions on Mathematical Software (TOMS), v.9 n.1, p.117-124, March 1983
	Ronald F. Boisvert, A fourth-order-accurate Fourier method for the Helmholtz equation in three dimensions, ACM Transactions on Mathematical Software (TOMS), v.13 n.3, p.221-234, Sept. 1987