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Showing 1 to 20 of 24 for “"multigrid method"”.
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Solving Buckling Problems and Computing Critical Points Using the Multigrid Method
… tangent stiffness operator which allows the multigrid method to function properly.
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Resolution of the adjoint Navier-Stokes equations using a preconditioned multigrid method
Las ecuaciones de Navier-Stokes adjuntas se resuelven con un método multimalla precondicionado. La utilización de este resolvedor se fundamenta en las mejoras de diseño que se obtienen con un método de optimización basado en el gradiente. El ahorro de tiempo que se consigue cuando se utiliza la …
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Parallel Multigrid Method for Adaptive Finite Elements with Application to 3D Flow Problems
Aim of this work is the examination of numerical methods for the solution of large systems of PDE's. The equations under consideration arise from chemically reacting flows. A focal point is the analysis of a finite element discretization with stabilized finite elements of degree two. Aspects of …
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A projected multigrid method for the solution of non-linear finite element problems on adaptively refined grids
… the formulation and application of an adaptive multigrid method for the efficient solution of nonlinear elliptic and parabolic partial differential equations and systems. A continuous Galerkin finite-element method is combined with locally adaptive mesh refinement and an optimal multigrid solver …
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Implicit Finite Element Contact With a Multigrid Solver on Parallel Computers
… linear solvers are attractive. The geometric multigrid method is an iterative linear equation solving method able to arrive at a solution after O(n) work. Enabling a multigrid method to work for a contact problem requires special treatment of the contact stiffness matrix on coarse meshes. This …
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Parallel multilevel procedures for elastoplasticity computations in solid mechanics
A multigrid method is described that can solve history dependent, material nonlinear solid mechanics problems using the finite element method. Specifically, an incremental Newton-Raphson procedure is used to linearize the nonlinear equilibrium equations. The multigrid method is then used to solve …
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Efficient solutions of 2-D incompressible steady laminar separated flows
… flows at moderate-to-high Reynolds numbers. The method uses an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function equations. Results are …
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A Portable and Scalable Multigrid Solver for Nonlinear Structural Mechanics Problems
… (MPI) is used to implement the proposed parallel multigrid method, which ensures the portability of the code. The object-based programming model adopted for this work is also described. The performance of the parallel algorithm is studied using two sets of benchmark problems: fixed-size problems …
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Multilevel solution procedures for structural dynamics eigenvalue problems
Three multigrid algorithms are described that can solve the symmetric generalized eigenvalue problem encountered in structural dynamics. First, the multigrid algorithm for solving linear matrix equations is incorporated into the subspace iteration and block Lanczos methods to produce implicit …
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Acceleration Techniques for Industrial Large Eddy Simulation with High-Order Methods on CPU-GPU Clusters
… LES. The high-order flux reconstruction (FR) method is used as the spatial discretization scheme. First, two acceleration techniques are investigated: the p-multigrid algorithm and Mach number preconditioning. The Weiss and Smith low Mach number preconditioner is used together with the …
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Variable Viscosity Thermal Convection at Infinite Prandtl Number in a Thick Spherical Shell
… shell is modeled using the finite element method. The discretized tensor Navier-Stokes equations are solved with the multigrid method applied to the spherical elements. Numerically convergent solutions can be obtained when specially tailored matrix dependent transfer is introduced in the …
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Mathematical modelling of evaporation mechanisms and instabilities in cryogenic liquids
… temperature and concentration equations and the multigrid method for the Poisson equation. From plots of the evolution of the system, it is found that convection becomes stronger when preferential evaporation is included. </p><p class="MsoNormal">This new model demonstrates how to include …
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Application of Helmholtz/Hodge Decomposition to Finite Element Methods for Two-Dimensional Maxwell's Equations
… equations and a brief survey of finite element methods for Maxwell's equations. Then we review the related fundamentals in Chapter 2. In Chapter 3, we discuss the related vector function spaces and the Helmholtz/Hodge decomposition which are used in Chapter 4 and 5. The new results in this …
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Thermal convection in slender laterally-heated cavities
… solutions are found using a DuFort-Frankel-Multigrid method, and appear to be in good agreement with theoretical predictions of a boundary-layer structure at high values of the Rayleigh number. For time-dependent shallow cavity flows, new theoretical solutions and numerical solutions are …
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Data parallel algebraic multigrid
Algebraic multigrid methods for large, sparse linear systems are central to many computational simulations. Parallel algorithms for such solvers are generally decomposed into coarse-grain tasks suitable for distributed computers with traditional processing cores. Accelerating multigrid methods on …
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The Parallel Performance and Implementation of an Adaptive Multigrid Algorithm
An adaptive multigrid algorithm has been implemented on shared memory parallel computers to solve large-scale structural mechanics problems. The solution algorithm begins by solving the problem on the initial mesh, refining this mesh as required by the chosen adaptive scheme, and then solving the …
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A Finite-Element Coarse-GridProjection Method for Incompressible Flows
Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping …
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Unified Multilevel Adaptive Finite Element Methods for Elliptic Problems
… through the uses of adaptive refinement and multigrid solution techniques. It is our goal to develop a more unified approach to the combined process of adaptive refinement and multigrid solution which can be used with high order finite elements. The basic step of the refinement process is the …
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Numerical simulations of die casting with uncertainty quantification and optimization using neural networks
… unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. Multiple case studies are presented by coupling surrogate models such as polynomial chaos expansion (PCE) and neural network with OpenCast for uncertainty …
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A numerical study into the effects of turbulent flows around full-scale buildings
… and a co-located variable-storage arrangement. A multigrid method was introduced and was found to reduce the computational time by nearly a factor of ten. Both the Reynolds-stress transport model and the non-linear k-€ model were implemented in a form suitable for use with body-fitted coordinates …
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