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FEM for integral equations
Posted Jun 19, 2010, 3:17 a.m. EDT 1 Reply
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Hello everybody,
After a few exchanges on this forum, I ask myself some questions about COMSOL.
1) I would like to know how COMSOL can solve an integral equation (just the algorithme) using the weak application mode.
For an PDE, I know that first COMSOL multiplies the PDE by a test function, and then integrates to obtain an integral equation formulation called the "weak form". After discretization of the geometry, the values of the function unknown are determined at the nodes of the mesh and then interpolated between nodes on each elements using shape functions... ok ! elementary principle of FEM.
About the integral equations. How does COMSOL can solve an integral equation using the weak application mode ? Does COMSOL proceed in the same manner as if it was an PDE ? I mean does it multiplies the integral equation by a function test, then integrates, then discretizes the geometriy to obtain a system of algebraic equations... ?
2) Is it possible to perform FEM using a collocation method ? I think that COMSOL just allows to use Galerkin method...I am right ?
Thank you for your help !
Sebastien
After a few exchanges on this forum, I ask myself some questions about COMSOL.
1) I would like to know how COMSOL can solve an integral equation (just the algorithme) using the weak application mode.
For an PDE, I know that first COMSOL multiplies the PDE by a test function, and then integrates to obtain an integral equation formulation called the "weak form". After discretization of the geometry, the values of the function unknown are determined at the nodes of the mesh and then interpolated between nodes on each elements using shape functions... ok ! elementary principle of FEM.
About the integral equations. How does COMSOL can solve an integral equation using the weak application mode ? Does COMSOL proceed in the same manner as if it was an PDE ? I mean does it multiplies the integral equation by a function test, then integrates, then discretizes the geometriy to obtain a system of algebraic equations... ?
2) Is it possible to perform FEM using a collocation method ? I think that COMSOL just allows to use Galerkin method...I am right ?
Thank you for your help !
Sebastien
1 Reply Last Post Jun 19, 2010, 7:31 a.m. EDT
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Posted:
1 decade ago
Hi
take the COMSOL courses on "advanced simualtions", and/or read trough some of the matematical books referred to in the documentation, or on the web site. These are the best references and explanations you can get, and then try out simple exercices with comsol, and compare it with your hand calculations.
The aim of COMSOL, in my view, is to take away the burden to know in detials all the maths behind, and concentrate on the physics, but I agree there are a minimum you need to know, and everyone has a different opinion on where this limit goes.
Bons maths avec Comsol
Et bon weekend
Ivar
take the COMSOL courses on "advanced simualtions", and/or read trough some of the matematical books referred to in the documentation, or on the web site. These are the best references and explanations you can get, and then try out simple exercices with comsol, and compare it with your hand calculations.
The aim of COMSOL, in my view, is to take away the burden to know in detials all the maths behind, and concentrate on the physics, but I agree there are a minimum you need to know, and everyone has a different opinion on where this limit goes.
Bons maths avec Comsol
Et bon weekend
Ivar