scholarly journals Comparison of high order finite element and discontinuous Galerkin methods for phase field equations: Application to structural damage

2017 ◽  
Vol 74 (7) ◽  
pp. 1542-1564 ◽  
Author(s):  
L.R. Chiarelli ◽  
F.G. Fumes ◽  
E.A. Barros de Moraes ◽  
G.A. Haveroth ◽  
J.L. Boldrini ◽  
...  
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Phase Field ◽  
Structural Damage ◽  
Discontinuous Galerkin Methods ◽  
High Order ◽  
Galerkin Methods ◽  
Field Equations ◽  
Phase Field Equations

scholarly journals Fast Tensor Product Schwarz Smoothers for High-Order Discontinuous Galerkin Methods

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Julius Witte ◽  
Daniel Arndt ◽  
Guido Kanschat
Keyword(s):  
Finite Element ◽  
Tensor Product ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Space Dimension ◽  
High Order ◽  
Low Rank ◽  
Galerkin Methods ◽  
Low Rank Representation ◽  
Subspace Correction Methods

AbstractWe discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high-order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices associated to mesh cells and to the patches around a vertex, respectively, in order to obtain fast local solvers for additive and multiplicative subspace correction methods. The effort of inverting local matrices for tensor product polynomials of degree k is reduced from {\mathcal{O}(k^{3d})} to {\mathcal{O}(dk^{d+1})} by exploiting the separability of the differential operator and resulting low rank representation of its inverse as a prototype for more general low rank representations in space dimension d.

High-Order Mesh Generation for Discontinuous Galerkin Methods Based on Elastic Deformation

2016 ◽  
Vol 8 (4) ◽  
pp. 693-702
Author(s):  
Hongqiang Lu ◽  
Kai Cao ◽  
Lechao Bian ◽  
Yizhao Wu
Keyword(s):  
Finite Element Method ◽  
Discontinuous Galerkin ◽  
Mesh Generation ◽  
Discontinuous Galerkin Methods ◽  
Elasticity Modulus ◽  
High Order ◽  
Galerkin Methods ◽  
Governing Equations ◽  
Numerical Tests ◽  
Cubic Polynomial

AbstractIn this paper, a high-order curved mesh generation method for Discontinuous Galerkin methods is introduced. First, a regular mesh is generated. Second, the solid surface is re-constructed using cubic polynomial. Third, the elastic governing equations are solved using high-order finite element method to provide a fully or partly curved grid. Numerical tests indicate that the intersection between element boundaries can be avoided by carefully defining the elasticity modulus.

High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation

2015 ◽  
Vol 71 (1) ◽  
pp. 181-206 ◽  
Author(s):  
Paola F. Antonietti ◽  
Carlo Marcati ◽  
Ilario Mazzieri ◽  
Alfio Quarteroni
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
High Order ◽  
Galerkin Methods
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