3,568 research outputs found
Classical and all-floating FETI methods for the simulation of arterial tissues
High-resolution and anatomically realistic computer models of biological soft
tissues play a significant role in the understanding of the function of
cardiovascular components in health and disease. However, the computational
effort to handle fine grids to resolve the geometries as well as sophisticated
tissue models is very challenging. One possibility to derive a strongly
scalable parallel solution algorithm is to consider finite element tearing and
interconnecting (FETI) methods. In this study we propose and investigate the
application of FETI methods to simulate the elastic behavior of biological soft
tissues. As one particular example we choose the artery which is - as most
other biological tissues - characterized by anisotropic and nonlinear material
properties. We compare two specific approaches of FETI methods, classical and
all-floating, and investigate the numerical behavior of different
preconditioning techniques. In comparison to classical FETI, the all-floating
approach has not only advantages concerning the implementation but in many
cases also concerning the convergence of the global iterative solution method.
This behavior is illustrated with numerical examples. We present results of
linear elastic simulations to show convergence rates, as expected from the
theory, and results from the more sophisticated nonlinear case where we apply a
well-known anisotropic model to the realistic geometry of an artery. Although
the FETI methods have a great applicability on artery simulations we will also
discuss some limitations concerning the dependence on material parameters.Comment: 29 page
Substructured formulations of nonlinear structure problems - influence of the interface condition
We investigate the use of non-overlapping domain decomposition (DD) methods
for nonlinear structure problems. The classic techniques would combine a global
Newton solver with a linear DD solver for the tangent systems. We propose a
framework where we can swap Newton and DD, so that we solve independent
nonlinear problems for each substructure and linear condensed interface
problems. The objective is to decrease the number of communications between
subdomains and to improve parallelism. Depending on the interface condition, we
derive several formulations which are not equivalent, contrarily to the linear
case. Primal, dual and mixed variants are described and assessed on a simple
plasticity problem.Comment: in International Journal for Numerical Methods in Engineering, Wiley,
201
Shifted Laplacian multigrid for the elastic Helmholtz equation
The shifted Laplacian multigrid method is a well known approach for
preconditioning the indefinite linear system arising from the discretization of
the acoustic Helmholtz equation. This equation is used to model wave
propagation in the frequency domain. However, in some cases the acoustic
equation is not sufficient for modeling the physics of the wave propagation,
and one has to consider the elastic Helmholtz equation. Such a case arises in
geophysical seismic imaging applications, where the earth's subsurface is the
elastic medium. The elastic Helmholtz equation is much harder to solve than its
acoustic counterpart, partially because it is three times larger, and partially
because it models more complicated physics. Despite this, there are very few
solvers available for the elastic equation compared to the array of solvers
that are available for the acoustic one. In this work we extend the shifted
Laplacian approach to the elastic Helmholtz equation, by combining the complex
shift idea with approaches for linear elasticity. We demonstrate the efficiency
and properties of our solver using numerical experiments for problems with
heterogeneous media in two and three dimensions
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