... | ... | @@ -4,126 +4,17 @@ When solving the EEG/MEG forward problems using DUNEuro, the source model parame |
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An overview of the different parameters is given below.
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# CG
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## partial integration
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name in config: `partial_integration`
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### parameters:
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- none
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### description:
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# Partial Integration
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Direct application of the distributional derivative of the dipolar source term to the test function. The resulting right hand side will have as many non-zero entries as the element containing the dipole has associated degrees of freedom (e.g. nodes for linear basis functions). For tetrahedral meshes, the partial integration approach is constant within each element.
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## vertex based monopolar venant
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name in config: `venant`
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### parameters:
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- todo
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### description:
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todo
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## patch based monopolar venant
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name in config: `patch_based_venant`
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### parameters:
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- todo
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### description:
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todo
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## spatial venant
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name in config: `spatial_venant`
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### parameters:
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- todo
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### description:
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todo
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## truncated spatial venant
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name in config: `truncated_spatial_venant`
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### parameters:
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- todo
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### description:
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todo
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## whitney
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name in config: `whitney`
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### parameters:
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- todo
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### description:
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todo
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## subtraction
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name in config: `subtraction`
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### parameters:
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- todo
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### description:
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todo
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# DG
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## partial integration
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name in config: `partial_integration`
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### parameters:
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- todo
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### description:
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todo
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## patch based monopolar venant
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name in config: `patch_based_venant`
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### parameters:
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- todo
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### description:
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todo
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## spatial venant
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name in config: `spatial_venant`
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### parameters:
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- todo
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### description:
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todo
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## subtraction
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name in config: `subtraction`
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### parameters:
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- todo
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### description:
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todo
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## localized subtraction
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name in config: `localized_subtraction`
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### parameters:
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- todo
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### description:
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todo
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# UDG
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## partial integration
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name in config: `partial_integration`
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### parameters:
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- todo
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### description:
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todo
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## monopolar venant
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name in config: `patch_based_venant`
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### parameters:
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- todo
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### description:
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todo
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# St. Venant
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The idea of the approach following St. Venant is to replace the dipolar source by a distribution of electrical monopoles which best reproduces the source moment.
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# CutFEM
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## partial integration
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name in config: `partial_integration`
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### parameters:
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- todo
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# Whitney
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For the Whitney source modeling approach, a source term with a higher regularity is
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chosen. The primary current $`j_p`$ is discretized in a vector-valued function space consisting of functions with square-integrable divergence.
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### description:
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todo |
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\ No newline at end of file |
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# Subtraction
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The subtraction approach relies on the assumption that there exists a small area around the dipole location, where the conductivity is constant. As a result, the potential and the conductivity can be split into two contributions, a singularity contribution and a correction part: $`u = u_\infty + u_{corr}`$, and $`\sigma = \sigma_\infty + \sigma_{corr}`$.
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While $`u_\infty`$ can be computed analytically, the insertion of the above decomposition into the EEG forward problem results in a Poisson equation for the correction potential with a right hand side $`- \nabla \cdot (\sigma_{corr} \nabla u_\infty)`$ and inhomogeneous Neumann boundary conditions. |