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Mederos, Victoria Hernández (author), Ugalde, Isidro Abelló (author), Alfonso, Rolando M.Bruno (author), Lahaye, D.J.P. (author), Ones, Valia Guerra (author)In this paper we use the Isogeometric Analysis (IgA) to solve the Helmholtz equation with Dirichlet boundary condition over a bounded physical 2D domain. Starting from the variational formulation of the problem, we show how to apply IgA to obtain an approximated solution based on biquadratic Bspline functions. We focus the attention on...journal article 2023
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Sieburgh, Erik (author)Wave phenomena play an important role in many different applications such as MRI scans, seismology and acoustics [41, 49, 47]. At the core of such applications lies the Helmholtz equation, which represents the timeindependent version of the wave equation. Simulating a Helmholtz problem numerically with accurate numerical solutions for large...master thesis 2022
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Dwarka, V.N.S.R. (author), Vuik, Cornelis (author)Recent research efforts aimed at iteratively solving timeharmonic waves have focused on a broad range of techniques to accelerate convergence. In particular, for the famous Helmholtz equation, deflation techniques have been studied to accelerate the convergence of Krylov subspace methods. In this work, we extend the twolevel deflation method...journal article 2022
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Dwarka, V.N.S.R. (author), Vuik, Cornelis (author)In researching the Helmholtz equation, the focus has either been on the accuracy of the numerical solution (pollution) or the acceleration of the convergence of a preconditioned Krylovbased solver (scalability). While it is widely recognized that the convergence properties can be investigated by studying the eigenvalues, information from the...journal article 2021
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Lok, Peter (author)Numerical modelling of high frequency waves is a complex and challenging area. Although the underlying equation seems simple, −∆φ − k2φ = f, the numerical challenges are not. This time harmonic wave equation is known as the Helmholtz equation. The main challenge to be studied is the pollution error, which is the difference between the actual and...master thesis 2020
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Dwarka, V.N.S.R. (author), Vuik, Cornelis (author)Recent research efforts aimed at iteratively solving the Helmholtz equation have focused on incorporating deation techniques for accelerating the convergence of Krylov subpsace methods. The requisite for these efforts lies in the fact that the widely used and wellacknowledged complex shifted Laplacian preconditioner (CSLP) shifts the...journal article 2020
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Meijers, Onno (author)To get a clear picture of the earth crust the Helmholtz equation needs to be<br/>solved and a high wave number is needed in order to provide fine grain details.<br/>The Stabilised BiConjugate Gradient method needs to be implemented to solve<br/>the Helmholtz equation. This is done on a Maxeler data flow machine to improve<br/>calculation times....master thesis 2017
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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, Cornelis (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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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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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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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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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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