scholarly journals An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids

2020 ◽  
Vol 89 (325) ◽  
pp. 2047-2083
Author(s):  
Paola F. Antonietti ◽  
Paul Houston ◽  
Giorgio Pennesi ◽  
Endre Süli
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
High Order ◽  
Massively Parallel ◽  
Galerkin Methods ◽  
Additive Schwarz ◽  
Schwarz Preconditioner

scholarly journals On Discontinuous Galerkin Methods for Elliptic Problems with Discontinuous Coefficients

2003 ◽  
Vol 3 (1) ◽  
pp. 76-85 ◽  
Author(s):  
Maksymilian Dryja
Keyword(s):  
Rate Of Convergence ◽  
Discontinuous Galerkin ◽  
Error Bound ◽  
Discontinuous Galerkin Methods ◽  
Elliptic Problems ◽  
Discontinuous Coefficients ◽  
Galerkin Methods ◽  
Additive Schwarz ◽  
Discrete Problems ◽  
Schwarz Preconditioner

AbstractDiscontinuous Galerkin methods for elliptic problems with discontinuous coefficients are discussed. First the error bound of the methods is analyzed. Then a multilevel additive Schwarz preconditioner for one of the discrete problems is designed and analyzed. Although the preconditioner is not optimal it is very well suited for parallel computations and its rate of convergence is independent of the jumps of coefficients.

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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