Every forward solve, adjoint solve and Jacobian of EIT is a sparse symmetric positive semidefinite system with several right-hand sides. This chapter covers direct and iterative solvers, preconditioners, and fast transform methods for structured domains.
Reading order.
- Krylov methods: Conjugate Gradient Method, Projected Conjugate Gradient for the singular Neumann problem, Block Conjugate Gradient for several patterns at once; MINRES, LSQR and Block Krylov Methods for related problems.
- Direct factorisation: Projected Cholesky Factorization.
- Preconditioning: Algebraic Multigrid.
- Fast transforms: Discrete Cosine Transform, Fast Solvers on Rectangular Domains, Fast Solvers on Disk Domains.
A comparison with recommendations is Choosing a Linear Solver.
Related. The null space and grounding are introduced in Finite Elements; mapping general domains to the disk in Meshes and Geometry.
References
- Y. Saad (2003). Iterative Methods for Sparse Linear Systems, 2nd ed. SIAM. doi:10.1137/1.9780898718003