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Tang, J.M. (author), Nabben, R. (author), Vuik, C. (author), Erlangga, Y.A. (author)For various applications, it is wellknown that a multilevel, in particular twolevel, preconditioned CG (PCG) method is an efficient method for solving large and sparse linear systems with a coefficient matrix that is symmetric positive definite. The corresponding twolevel preconditioner combines traditional and projectiontype...journal article 2009
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 Tang, J.M. (author), Nabben, R. (author), Vuik, C. (author), Erlangga, Y.A. (author) report 2007
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Erlangga, Y.A. (author)This paper discusses an iterative method for solving the Helmholtz equation with the perfectly matched layer (PML). The method consists of an outer and inner iteration process. The inner iteration is used to approximately solve a preconditioner, which in this case is based on a modified PML equation. The outer iteration is a Krylov subspace...conference paper 2006
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Van Gijzen, M.B. (author), Erlangga, Y.A. (author)By combining elementbyelement estimates for the field of values of a preconditioned matrix with GMRESconvergence estimates it is possible to derive an easily computable upper bound on the GMRESresidual norm. This method can be applied to general finite element systems, but the preconditioner has to be Hermitian and positive definite. The...conference paper 2006
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Turkel, E. (author), Erlangga, Y.A. (author)We consider acoustic scattering about a general body. This is described by the Helmholtz equation exterior to the body. In order to truncate the infinite domain we use the BGT absorbing boundary condition. The resultant problem in a finite domain is solved by a finite element procedure. This yields a large sparse system of linear equations which...conference paper 2006
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Van Gijzen, M.B. (author), Erlangga, Y.A. (author)By combining elementbyelement estimates for the field of values of a preconditioned matrix with GMRESconvergence estimates it is possible to derive an easily computable upper bound on the GMRESresidual norm. This method can be applied to general finite element systems, but the preconditioner has to be Hermitian and positive definite. The...conference paper 2006
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Riyanti, C.D. (author), Erlangga, Y.A. (author), Plessix, R.E. (author), Mulder, W.A. (author), Vuik, C. (author), Oosterlee, C. (author)The timeharmonic wave equation, also known as the Helmholtz equation, is obtained if the constantdensity acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In...journal article 2006
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van Gijzen, M.B. (author), Erlangga, Y.A. (author), Vuik, C. (author)Shifted Laplace preconditioners have attracted considerable attention as a technique to speed up convergence of iterative solution methods for the Helmholtz equation. In this paper we present a comprehensive spectral analysis of the Helmholtz operator preconditioned with a shifted Laplacian. Our analysis is valid under general conditions. The...report 2006
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 Erlangga, Y.A. (author) doctoral thesis 2005
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Erlangga, Y.A. (author), Oosterlee, C.W. (author), Vuik, C. (author)An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the...report 2004
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 Erlangga, Y.A. (author), Vuik, C. (author), Oosterlee, C.W. (author) report 2003
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 Vuik, C. (author), Erlangga, Y.A., Oosterlee, C.W. (author) report 2003
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Erlangga, Y.A. (author)In this report, several numerical aspects and diculties for solving a linear system derived from the timeharmonic wave equations are overviewed. The presentation begins with the derivation of the governing equation for waves propagating in general inhomogeneous media. Due to the need of numerical solutions, various discretizations based on...report 2002