Skip to main content
MathOverflow

Return to Question

Bumped by Community user
Bumped by Community user
Bumped by Community user
small fixfdfdf
Source Link
Leo Alonso
Leo Alonso
  • 9.2k
  • 2
  • 43
  • 57

I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$
Insulator (Neumann BC)
Electrode set at some potential (Dirichlet BC).
Additionally I have some electrodes $E_l$ which are set to have a fixed current $I_l$, so on these the boundary condition is $\int_{E_l} \sigma(x,y,z)(du/dn) dA=I_l$.

How would I go about incoprorating this third type of BC into FEM? Any description or references is what im looking for.

Additionaly or altenrativelyalternatively, I would like to know if there is some way to obtain accurate flux computations over surfaces in FEM. The normal way to solve Poisson equation using FEM does not give very accurate fluxes, however commercial software using FEM does, does anyone know how they do it? I am looking for references on how to compute such accurate fluxes.

I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$
Insulator (Neumann BC)
Electrode set at some potential (Dirichlet BC).
Additionally I have some electrodes $E_l$ which are set to have a fixed current $I_l$, so on these the boundary condition is $\int_{E_l} \sigma(x,y,z)(du/dn) dA=I_l$.

How would I go about incoprorating this third type of BC into FEM? Any description or references is what im looking for.

Additionaly or altenratively, I would like to know if there is some way to obtain accurate flux computations over surfaces in FEM. The normal way to solve Poisson equation using FEM does not give very accurate fluxes, however commercial software using FEM does, does anyone know how they do it? I am looking for references on how to compute such accurate fluxes.

I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$
Insulator (Neumann BC)
Electrode set at some potential (Dirichlet BC).
Additionally I have some electrodes $E_l$ which are set to have a fixed current $I_l$, so on these the boundary condition is $\int_{E_l} \sigma(x,y,z)(du/dn) dA=I_l$.

How would I go about incoprorating this third type of BC into FEM? Any description or references is what im looking for.

Additionaly or alternatively, I would like to know if there is some way to obtain accurate flux computations over surfaces in FEM. The normal way to solve Poisson equation using FEM does not give very accurate fluxes, however commercial software using FEM does, does anyone know how they do it? I am looking for references on how to compute such accurate fluxes.

small fixfdfdf
Source Link
edit approved May 3, 2017 at 8:28
Grandmaster Bator
edit approved May 3, 2017 at 8:28
Grandmaster Bator
  • 3
  • 1

I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$
Insulator (Neumann BC)
Electrode set at some potential (Dirichlet BC).
Additionally I have some electrodes $E_l$ which are set to have a fixed current $I_l$, so on these the boundary condition is $\int_{E_l} \sigma(du/dn) ds=I_l$$\int_{E_l} \sigma(x,y,z)(du/dn) dA=I_l$.

How would I go about incoprorating this third type of BC into FEM? Any description or references is what im looking for.

If this is impossibleAdditionaly or too hardaltenratively, I would like to know if there is some way to obtain accurate flux computations over surfaces in FEM. The normal way to solve Poisson equation using FEM does not give very accurate fluxes, however commercial software using FEM does, does anyone know how they do it? I am looking for references on how to compute such accurate fluxes.

I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$
Insulator (Neumann BC)
Electrode set at some potential (Dirichlet BC).
Additionally I have some electrodes $E_l$ which are set to have a fixed current $I_l$, so on these the boundary condition is $\int_{E_l} \sigma(du/dn) ds=I_l$.

How would I go about incoprorating this third type of BC into FEM? Any description or references is what im looking for.

If this is impossible or too hard, I would like to know if there is some way to obtain accurate flux computations over surfaces in FEM. The normal way to solve Poisson equation using FEM does not give very accurate fluxes, however commercial software using FEM does, does anyone know how they do it? I am looking for references on how to compute such accurate fluxes.

I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$
Insulator (Neumann BC)
Electrode set at some potential (Dirichlet BC).
Additionally I have some electrodes $E_l$ which are set to have a fixed current $I_l$, so on these the boundary condition is $\int_{E_l} \sigma(x,y,z)(du/dn) dA=I_l$.

How would I go about incoprorating this third type of BC into FEM? Any description or references is what im looking for.

Additionaly or altenratively, I would like to know if there is some way to obtain accurate flux computations over surfaces in FEM. The normal way to solve Poisson equation using FEM does not give very accurate fluxes, however commercial software using FEM does, does anyone know how they do it? I am looking for references on how to compute such accurate fluxes.

Source Link
Pelle
Pelle
  • 11
  • 2

How to solve Poissons equation using FEM with integral BC?

I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$
Insulator (Neumann BC)
Electrode set at some potential (Dirichlet BC).
Additionally I have some electrodes $E_l$ which are set to have a fixed current $I_l$, so on these the boundary condition is $\int_{E_l} \sigma(du/dn) ds=I_l$.

How would I go about incoprorating this third type of BC into FEM? Any description or references is what im looking for.

If this is impossible or too hard, I would like to know if there is some way to obtain accurate flux computations over surfaces in FEM. The normal way to solve Poisson equation using FEM does not give very accurate fluxes, however commercial software using FEM does, does anyone know how they do it? I am looking for references on how to compute such accurate fluxes.