Comparing Iterative Solvers for Linear Systems associated with the Finite Difference Discretisation of the Forward Problem in Electroencephalographic Source Analysis

Model-based reconstruction of electrical brain activity from electroencephalographic measurements is of growing importance in neurology and neurosurgery. Algorithms for this task involve the solution of a 3D Poisson problem on a realistic head geometry obtained from medical imaging. In the model, several compartments with different conductivities have to be distinguished, leading to a problem with jumping coefficients. Furthermore, Poisson's problem needs to be solved repeatedly for different source contributions. Thus efficient solvers for this subtask are required. We report on our experience with different iterative solvers: successive over-relaxation, (preconditioned) conjugate gradients, and algebraic multigrid, for a discretisation based on cell-centred finite-differences. We found that (a) the multigrid-based solver performed the task 1.8-3.5 times faster, platform depending, than the second-best contender, (b) there is no need to introduce a reference potential which forces a unique solution and (c) neither the grid- nor matrix-based implementation of the solvers consistently gives a smaller run time.

@article{id445,
  author = {Mohr, M. and Vanrumste, B.},
  doi = {10.1007/bf02343542},
  journal = {Mathematical and Biological Engineering and Computing},
  language = {en},
  number = {1},
  pages = {75{\textendash}84},
  title = {Comparing Iterative Solvers for Linear Systems associated with the Finite Difference Discretisation of the Forward Problem in Electroencephalographic Source Analysis},
  volume = {41},
  year = {2003},
}

%O Journal Article
%A Mohr, M.
%A Vanrumste, B.
%R 10.1007/bf02343542
%J Mathematical and Biological Engineering and Computing
%G en
%N 1
%P 75–84
%T Comparing Iterative Solvers for Linear Systems associated with the Finite Difference Discretisation of the Forward Problem in Electroencephalographic Source Analysis
%V 41
%D 2003