scholarly journals Semi-implicit Non-conforming Finite-Element Schemes for Cardiac Electrophysiology: A Framework for Mesh-Coarsening Heart Simulations

2018 ◽  
Vol 9 ◽  
Author(s):  
Javiera Jilberto ◽  
Daniel E. Hurtado
Keyword(s):  
Finite Element ◽  
Cardiac Electrophysiology ◽  
Conforming Finite Element ◽  
Finite Element Schemes ◽  
Mesh Coarsening

scholarly journals Description and implementation of an algebraic multigrid preconditioner for H1-conforming finite element schemes

Uniciencia ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 55-81
Author(s):  
Helen Guillén-Oviedo ◽  
Jeremías Ramírez-Jiménez ◽  
Esteban Segura-Ugalde ◽  
Filánder Sequeira-Chavarría
Keyword(s):  
Finite Element ◽  
Numerical Experiments ◽  
Mesh Size ◽  
Algebraic Multigrid ◽  
The Finite Element Method ◽  
Conforming Finite Element ◽  
Finite Element Schemes ◽  
Pcg Method ◽  
Continuous Problem ◽  
Number Of Iterations

This paper presents detailed aspects regarding the implementation of the Finite Element Method (FEM) to solve a Poisson’s equation with homogeneous boundary conditions. The aim of this paper is to clarify details of this implementation, such as the construction of algorithms, implementation of numerical experiments, and their results. For such purpose, the continuous problem is described, and a classical FEM approach is used to solve it. In addition, a multilevel technique is implemented for an efficient resolution of the corresponding linear system, describing and including some diagrams to explain the process and presenting the implementation codes in MATLAB®. Finally, codes are validated using several numerical experiments. Results show an adequate behavior of the preconditioner since the number of iterations of the PCG method does not increase, even when the mesh size is reduced.

scholarly journals $$H^1$$-conforming finite element cochain complexes and commuting quasi-interpolation operators on Cartesian meshes

CALCOLO ◽  
2021 ◽  
Vol 58 (2) ◽  
Author(s):  
Francesca Bonizzoni ◽  
Guido Kanschat
Keyword(s):  
Finite Element ◽  
Tensor Product ◽  
Arbitrary Order ◽  
Inner Product ◽  
Cochain Complex ◽  
Exterior Derivative ◽  
Product Construction ◽  
Cartesian Meshes ◽  
Conforming Finite Element ◽  
Interpolation Operators

AbstractA finite element cochain complex on Cartesian meshes of any dimension based on the $$H^1$$ H 1 -inner product is introduced. It yields $$H^1$$ H 1 -conforming finite element spaces with exterior derivatives in $$H^1$$ H 1 . We use a tensor product construction to obtain $$L^2$$ L 2 -stable projectors into these spaces which commute with the exterior derivative. The finite element complex is generalized to a family of arbitrary order.

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