999 research outputs found
Lmit and shakedown analysis based on solid shell models
The paper treats the formulation of the shakedown problem and, as special case, of the limit analysis problem, using solid shell models and ES-FEM discratization technology. In this proposal the Discrete shear gap method is applied to alleviate the shear locking phenomenon
Petri Nets Modeling of Dead-End Refinement Problems in a 3D Anisotropic hp-Adaptive Finite Element Method
We consider two graph grammar based Petri nets models for anisotropic refinements of three dimensional hexahedral grids. The first one detects possible dead-end problems during the graph grammar based anisotropic refinements of the mesh. The second one employs an enhanced graph grammar model that is actually dead-end free. We apply the resulting algorithm to the simulation of resistivity logging measurements for estimating the location of underground oil and/or gas formations. The graph grammar based Petri net models allow to fix the self-adaptive mesh refinement algorithm and finish the adaptive computations with the required accuracy needed by the numerical solution
Petri Nets Modeling of Dead-End Refinement Problems in a 3D Anisotropic hp-Adaptive Finite Element Method
We consider two graph grammar based Petri nets models for anisotropic refinements of three dimensional hexahedral grids. The first one detects possible dead-end problems during the graph grammar based anisotropic refinements of the mesh. The second one employs an enhanced graph grammar model that is actually dead-end free. We apply the resulting algorithm to the simulation of resistivity logging measurements for estimating the location of underground oil and/or gas formations. The graph grammar based Petri net models allow to fix the self-adaptive mesh refinement algorithm and finish the adaptive computations with the required accuracy needed by the numerical solution
An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids
In this article we design and analyze a class of two-level non-overlapping
additive Schwarz preconditioners for the solution of the linear system of
equations stemming from discontinuous Galerkin discretizations of second-order
elliptic partial differential equations on polytopic meshes. The preconditioner
is based on a coarse space and a non-overlapping partition of the computational
domain where local solvers are applied in parallel. In particular, the coarse
space can potentially be chosen to be non-embedded with respect to the finer
space; indeed it can be obtained from the fine grid by employing agglomeration
and edge coarsening techniques. We investigate the dependence of the condition
number of the preconditioned system with respect to the diffusion coefficient
and the discretization parameters, i.e., the mesh size and the polynomial
degree of the fine and coarse spaces. Numerical examples are presented which
confirm the theoretical bounds
Energy-based comparison between the Fourier--Galerkin method and the finite element method
The Fourier-Galerkin method (in short FFTH) has gained popularity in
numerical homogenisation because it can treat problems with a huge number of
degrees of freedom. Because the method incorporates the fast Fourier transform
(FFT) in the linear solver, it is believed to provide an improvement in
computational and memory requirements compared to the conventional finite
element method (FEM). Here, we systematically compare these two methods using
the energetic norm of local fields, which has the clear physical interpretation
as being the error in the homogenised properties. This enables the comparison
of memory and computational requirements at the same level of approximation
accuracy. We show that the methods' effectiveness relies on the smoothness
(regularity) of the solution and thus on the material coefficients. Thanks to
its approximation properties, FEM outperforms FFTH for problems with jumps in
material coefficients, while ambivalent results are observed for the case that
the material coefficients vary continuously in space. FFTH profits from a good
conditioning of the linear system, independent of the number of degrees of
freedom, but generally needs more degrees of freedom to reach the same
approximation accuracy. More studies are needed for other FFT-based schemes,
non-linear problems, and dual problems (which require special treatment in FEM
but not in FFTH).Comment: 24 pages, 10 figures, 2 table
- …