scholarly journals Towards a complete FEM-based simulation toolkit on GPUs: Unstructured grid finite element geometric multigrid solvers with strong smoothers based on sparse approximate inverses

2013 ◽  
Vol 80 ◽  
pp. 327-332 ◽  
Author(s):  
M. Geveler ◽  
D. Ribbrock ◽  
D. Göddeke ◽  
P. Zajac ◽  
S. Turek
Keyword(s):  
Finite Element ◽  
Unstructured Grid ◽  
Multigrid Solvers ◽  
Approximate Inverses ◽  
Geometric Multigrid

A finite element method for unstructured grid smoothing

2004 ◽  
Vol 194 (2) ◽  
pp. 611-631 ◽  
Author(s):  
Glen Hansen ◽  
Andrew Zardecki ◽  
Doran Greening ◽  
Randy Bos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Unstructured Grid ◽  
Element Method

scholarly journals Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs

2004 ◽  
Vol 26 (1) ◽  
pp. 31-54 ◽  
Author(s):  
H. De Sterck ◽  
Thomas A. Manteuffel ◽  
Stephen F. McCormick ◽  
Luke Olson
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
Algebraic Multigrid ◽  
Hyperbolic Pdes ◽  
Multigrid Solvers

A finite element particle code on an unstructured grid

1990 ◽  
Author(s):  
J. Ambrosiano ◽  
S. Brandon ◽  
R. Lohner
Keyword(s):  
Finite Element ◽  
Unstructured Grid

Anisotropic Modeling with Geometric Multigrid Preconditioned Finite Element Method

Geophysics ◽  
2022 ◽  
pp. 1-21
Author(s):  
Qingtao Sun ◽  
Runren Zhang ◽  
Ke Chen ◽  
Naixing Feng ◽  
Yunyun Hu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Scale ◽  
Data Interpretation ◽  
Scale Modeling ◽  
Arbitrary Anisotropy ◽  
Large Scale Modeling ◽  
Element Method ◽  
Geometric Multigrid ◽  
Electromagnetic Surveys

Formation anisotropy in complicated geophysical environments can have a significant impact on data interpretation of electromagnetic surveys. To facilitate full 3D modeling of arbitrary anisotropy, we have adopted an h-version geometric multigrid preconditioned finite-element method based on vector basis functions. By using a structured mesh, instead of an unstructured one, our method can conveniently construct the restriction and prolongation operators for multigrid implementation, and then recursively coarsen the grid with the F-cycle coarsening scheme. The geometric multigrid method is used as a preconditioner for the biconjugate-gradient stabilized method to efficiently solve the linear system resulting from the finite-element method. Our method avoids the need of interpolation for arbitrary anisotropy modeling as in Yee’s grid-based finite-difference method, and it is also more capable of large-scale modeling with respect to the p-version geometric multigrid preconditioned finite-element method. A numerical example in geophysical well logging is included to demonstrate its numerical performance. Our h-version geometric multigrid preconditioned finite-element method is expected to help formation anisotropy characterization with electromagnetic surveys in complicated geophysical environments.

A package for unstructured grid generation and finite element flow solvers

1989 ◽  
Author(s):  
CLYDE GUMBERT ◽  
RAINALD LOHNER ◽  
PARESH PARIKH ◽  
SHAHYAR PIRZADEH
Keyword(s):  
Finite Element ◽  
Unstructured Grid ◽  
Grid Generation
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