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Meijers, Onno (author)To get a clear picture of the earth crust the Helmholtz equation needs to bemaster thesis 2017
solved and a high wave number is needed in order to provide fine grain details.
The Stabilised BiConjugate Gradient method needs to be implemented to solve
the Helmholtz equation. This is done on a Maxeler data flow machine to improve
calculation times....
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Qiu, Y. (author), van Gijzen, M.B. (author), van Wingerden, J.W. (author), Verhaegen, M. (author), Vuik, C. (author)Multilevel sequentially semiseparable (MSSS) matrices form a class of structured matrices that have lowrank offdiagonal structure, which allows the matrixmatrix operations to be performed in linear computational complexity. MSSS preconditioners are computed by replacing the Schur complements in the block LU factorization of the global linear...report 2015
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Knibbe, H. (author), Vuik, C. (author), Oosterlee, C.W. (author)In geophysical applications, the interest in leastsquares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of highperformance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The...journal article 2015
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Knibbe, H.P. (author), Vuik, C. (author), Oosterlee, C.W. (author)In geophysical applications, the interest in leastsquares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of highperformance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The...journal article 2015
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Caratelli, D. (author), Gielis, J. (author), Tavkhelidze, I. (author), Ricci, P.E. (author)The Robin problem for the Helmholtz equation in normalpolar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the socalled “superformula” introduced by Gielis. A dedicated numerical procedure...journal article 2013
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Caratelli, D. (author), Gielis, J. (author), Natalini, P. (author), Ricci, P.E. (author), Tavkhelidze, I. (author)The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourierlike technique. Attention is in particular focused on normalpolar domains whose boundaries are defined by the socalled “superformula” introduced by J. Gielis. A dedicated numerical procedure based on the...journal article 2011
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Schakel, M.D. (author), Smeulders, D. (author)The dispersion relation for seismoelectric wave propagation in poroelastic media is formulated in terms of effective densities comprising all viscous and electrokinetic coupling effects. Using Helmholtz decomposition, two seismoelectric conversion coefficients are derived, for an incident Pwave upon an interface between a compressible fluid and...journal article 2010
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Gross, J. (author)A Helmholtz energy functional for inhomogeneous fluid phases based on the perturbedchain polar statistical associating fluid theory (PCPSAFT) equation of state is proposed. The model is supplemented with a capillary wave contribution to the surface tension to account for longwavelength fluctuations of a vaporliquid interface. The functional...journal article 2009
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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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Ito, K. (author), Toivanen, J. (author)The timeharmonic acoustic scattering in multilayered media is modeled with an inhomogeneous Helmholtz equation for the pressure field. For example, such problems result from acoustic geological surveys. The exterior problem is truncated into a rectangle and an absorbing boundary condition is posed on its boundaries. A loworder finite...conference paper 2006
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Otto, K. (author), Larsson, E. (author)A flexible solver for the Helmholtz equation is presented. The implementation of the solver is done in an objectoriented style, allowing for easy adaptation to different application problems. The solution methods that are employed are fast compared with standard solution techniques. The viability of the solver is demonstrated for realistic...conference paper 2006
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Schenk, O. (author), Bollhöfer, M. (author), Grote, M.J. (author)We propose efficient algebraic multilevel preconditioning for the Helmholtz equation with high wave numbers. Our method is mainly based on using new multilevel ILU techniques for symmetric indefinite systems. The method is mainly based on three major ingredients: 1. symmetric maximum weight matchings to increase the block di agonal dominance of...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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Heikkola, E. (author), Mönkölä, S. (author), Pennanen, A. (author), Rossi, T. (author)We consider the use of controllability techniques to solve the Helmholtz equation. Instead of solving directly the timeharmonic equation, we return to the corresponding timedependent equation and look for timeperiodic solution. The convergence is accelerated with a control technique by representing the original timeharmonic equation as an...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), 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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 Sampaio, E.E.S. (author), Fokkema, J.T. (author) journal article 1992