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Bangera, Sankalp (author)Composite structures are rapidly transforming the aerospace industry, driven by continuous advancements in manufacturing methods capable of producing optimized structures with variable stiffness that enables the creation of increasingly complex and efficient structures. This project focuses on the development of a global optimization method that...master thesis 2023
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Vandenplas, Jeremie (author), Nguyen, B. (author), Vuik, Cornelis (author)In this paper, we consider a block Jacobi preconditioner and various deflation techniques applied in the Deflated Preconditioned Conjugate Gradient (DPCG) method for solving a sparse system of linear equations derived from a statistical linear mixed model that analyses simultaneously phenotypic and pedigree information of genotyped and...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 time-independent 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)The bottleneck in designing iterative solvers for the Helmholtz equation lies in balancing the trade-off between accuracy and scalability. Both the accuracy of the numerical solution and the number of iterations to reach convergence deteriorate in higher dimensions and increase with the wavenumber. To address these issues in this dissertation,...doctoral thesis 2022
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Hoofwijk, Jorn (author)In finite element software one has to solve a system of non-linear equations, which is commonly simplified to a sequence of linear system. We research the possibility to solve these systems on a GPU to improve the solve time. We are particularly interested in systems arising from geotechnical models. We compare several combinations of Krylov...master thesis 2022
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Breunissen, Rens (author)Numerical methods for solving problems with a large contrast in the coefficients are investigated in this report. These types of problems typically appear in basin modeling. Specifically, the deflation and restricted additive Schwarz (RAS) methods are compared for their effectiveness in solving this type of problem in combination with the...master thesis 2022
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Dwarka, V.N.S.R. (author), Vuik, Cornelis (author)Recent research efforts aimed at iteratively solving time-harmonic 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 two-level deflation method...journal article 2022
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Schumann, Julian (author)High-dimensional optimization problems with expensive and non-convex cost functions pose a significant challenge, as the non-convexity limits the viability of local optimization, where the results are sensitive to initial guesses and often only represent local minima. But as the number of expensive cost function evaluations required for a full...master thesis 2021
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Maquelin, Eva (author)Numerical methods are investigated for solving large-scale sparse linear systems of equations, that can be applied to thermo-mechanical models and wafer-slip models. This thesis examines efficient numerical methods, in terms of memory, number of iterations required for convergence, and computation time. To be more specific, algebraic multigrid ...master thesis 2021
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Dwarka, V.N.S.R. (author), Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA)...journal article 2021
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Diaz Cortes, Gabriela Berenice (author), Vuik, Cornelis (author), Jansen, J.D. (author)We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to...journal article 2021
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Xia, Jingmin (author), Farrell, Patrick E. (author), Castro, Saullo G.P. (author)When loading experiments are repeated on different samples, qualitatively different results can occur. This is due to factors such as geometric imperfections, load asymmetries, unevenly stressed regions or uneven material distributions created by manufacturing processes. This fact makes designing robust thin-walled structures difficult. One...journal article 2020
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Zoutendijk, Mike (author)Structure Optimization has been an important subject with many applications for centuries. In the last sixty years, numerical optimization has facilitated large advancements in this field. One of the areas in Structure Optimization is Topology Optimization, which is used for Additive Manufacturing purposes. In this thesis we explore Static and...master thesis 2019
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Diaz Cortes, G.B. (author)Simulation of flow through highly heterogeneous porous media results in large ill-conditioned systems of equations. In particular, solving the linearized pressure system can be especially time-consuming. Therefore, extensive efforts to find ways to address this issue effectively are required. In this work, we introduce a POD-based deflation...doctoral thesis 2019
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Tjan, Jenny (author)We investigate the simulation of one-phase and two-phase flow through heterogeneous porous media.The derived matrix, resulting from reservoir simulation of groundwater flow problems, can result in a large and ill-conditioned system, i.e. the matrix has a high condition number, and the modelling takes large computation time. In this thesis report...master thesis 2018
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Diaz Cortes, G.B. (author), Vuik, Cornelis (author), Jansen, J.D. (author)We study fast and robust iterative solvers for large systems of linear equations resulting from simulation of flow trough strongly heterogeneous porous media. We propose the use of preconditioning and deflation techniques, based on information obtained frfrom the system, to reduce the time spent in the solution of the linear system.An important...journal article 2018
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Boitcov, Dmitrii (author)Existing multiscale solvers use a sequence of aggressive restriction, coarse-grid correction and prolongation operators to handle low-frequency modes on the coarse grid. High-frequency errors are resolved by employing a smoother on the fine grid. Deflation preconditioning improves matrix properties, i.e., damps slowly varying errors,...master thesis 2017
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- Sangers, A. (author) master thesis 2014
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Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), MacLachlan, S. (author), Vuik, C. (author), Scarpas, A. (author)Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms....journal article 2012
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Xu, S. (author)This thesis deals with two research problems. The first research problem is motivated by the numerical computation involved in the Time Domain Simulation (TDS) of Power Grids. Due to the ever growing size and complexity of Power Grids such as the China National Grid, accelerating TDS has become a stringent need for the online analysis of these...doctoral thesis 2011
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