1,275 research outputs found
Efficient implicit FEM simulation of sheet metal forming
For the simulation of industrial sheet forming processes, the time discretisation is\ud
one of the important factors that determine the accuracy and efficiency of the algorithm. For\ud
relatively small models, the implicit time integration method is preferred, because of its inherent\ud
equilibrium check. For large models, the computation time becomes prohibitively large and, in\ud
practice, often explicit methods are used. In this contribution a strategy is presented that enables\ud
the application of implicit finite element simulations for large scale sheet forming analysis.\ud
Iterative linear equation solvers are commonly considered unsuitable for shell element models.\ud
The condition number of the stiffness matrix is usually very poor and the extreme reduction\ud
of CPU time that is obtained in 3D bulk simulations is not reached in sheet forming simulations.\ud
Adding mass in an implicit time integration method has a beneficial effect on the condition number.\ud
If mass scaling is usedâlike in explicit methodsâiterative linear equation solvers can lead\ud
to very efficient implicit time integration methods, without restriction to a critical time step and\ud
with control of the equilibrium error in every increment. Time savings of a factor of 10 and more\ud
can easily be reached, compared to the use of conventional direct solvers.\ud
A Multigrid Optimization Algorithm for the Numerical Solution of Quasilinear Variational Inequalities Involving the -Laplacian
In this paper we propose a multigrid optimization algorithm (MG/OPT) for the
numerical solution of a class of quasilinear variational inequalities of the
second kind. This approach is enabled by the fact that the solution of the
variational inequality is given by the minimizer of a nonsmooth energy
functional, involving the -Laplace operator. We propose a Huber
regularization of the functional and a finite element discretization for the
problem. Further, we analyze the regularity of the discretized energy
functional, and we are able to prove that its Jacobian is slantly
differentiable. This regularity property is useful to analyze the convergence
of the MG/OPT algorithm. In fact, we demostrate that the algorithm is globally
convergent by using a mean value theorem for semismooth functions. Finally, we
apply the MG/OPT algorithm to the numerical simulation of the viscoplastic flow
of Bingham, Casson and Herschel-Bulkley fluids in a pipe. Several experiments
are carried out to show the efficiency of the proposed algorithm when solving
this kind of fluid mechanics problems
Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach
We develop a rigid multiblob method for numerically solving the mobility
problem for suspensions of passive and active rigid particles of complex shape
in Stokes flow in unconfined, partially confined, and fully confined
geometries. As in a number of existing methods, we discretize rigid bodies
using a collection of minimally-resolved spherical blobs constrained to move as
a rigid body, to arrive at a potentially large linear system of equations for
the unknown Lagrange multipliers and rigid-body motions. Here we develop a
block-diagonal preconditioner for this linear system and show that a standard
Krylov solver converges in a modest number of iterations that is essentially
independent of the number of particles. For unbounded suspensions and
suspensions sedimented against a single no-slip boundary, we rely on existing
analytical expressions for the Rotne-Prager tensor combined with a fast
multipole method or a direct summation on a Graphical Processing Unit to obtain
an simple yet efficient and scalable implementation. For fully confined
domains, such as periodic suspensions or suspensions confined in slit and
square channels, we extend a recently-developed rigid-body immersed boundary
method to suspensions of freely-moving passive or active rigid particles at
zero Reynolds number. We demonstrate that the iterative solver for the coupled
fluid and rigid body equations converges in a bounded number of iterations
regardless of the system size. We optimize a number of parameters in the
iterative solvers and apply our method to a variety of benchmark problems to
carefully assess the accuracy of the rigid multiblob approach as a function of
the resolution. We also model the dynamics of colloidal particles studied in
recent experiments, such as passive boomerangs in a slit channel, as well as a
pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201
Performance Portable Solid Mechanics via Matrix-Free -Multigrid
Finite element analysis of solid mechanics is a foundational tool of modern
engineering, with low-order finite element methods and assembled sparse
matrices representing the industry standard for implicit analysis. We use
performance models and numerical experiments to demonstrate that high-order
methods greatly reduce the costs to reach engineering tolerances while enabling
effective use of GPUs. We demonstrate the reliability, efficiency, and
scalability of matrix-free -multigrid methods with algebraic multigrid
coarse solvers through large deformation hyperelastic simulations of multiscale
structures. We investigate accuracy, cost, and execution time on multi-node CPU
and GPU systems for moderate to large models using AMD MI250X (OLCF Crusher),
NVIDIA A100 (NERSC Perlmutter), and V100 (LLNL Lassen and OLCF Summit),
resulting in order of magnitude efficiency improvements over a broad range of
model properties and scales. We discuss efficient matrix-free representation of
Jacobians and demonstrate how automatic differentiation enables rapid
development of nonlinear material models without impacting debuggability and
workflows targeting GPUs
Mini-Workshop: Interface Problems in Computational Fluid Dynamics
Multiple difficulties are encountered when designing algorithms to simulate flows having free surfaces, embedded particles, or elastic containers. One difficulty common to all of these problems is that the associated interfaces are Lagrangian in character, while the fluid equations are naturally posed in the Eulerian frame. This workshop explores different approaches and algorithms developed to resolve these issues
Schnelle Löser fĂŒr Partielle Differentialgleichungen
The workshop Schnelle Löser fĂŒr partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch (Leipzig), and Gabriel Wittum (Frankfurt am Main), was held May 22ndâMay 28th, 2011. This meeting was well attended by 54 participants with broad geographic representation from 7 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds
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