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- ItemA multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Schlundt, RainerThis paper describes a multilevel preconditioning technique for solving complex symmetric sparse linear systems. The coefficient matrix is first decoupled by domain decomposition and then an approximate inverse of the original matrix is computed level by level. This approximate inverse is based on low rank approximations of the local Schur complements. For this, a symmetric singular value decomposition of a complex symmetric matix is used. The block-diagonal matrices are decomposed by an incomplete LDLT factorization with the Bunch-Kaufman pivoting method. Using the example of Maxwells equations the generality of the approach is demonstrated.
- ItemA multilevel Schur complement preconditioner for complex symmetric matrices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Schlundt, RainerThis paper describes a multilevel preconditioning technique for solving complex symmetric sparse linear systems. The coefficient matrix is first decoupled by domain decomposition and then an approximate inverse of the original matrix is computed level by level. This approximate inverse is based on low rank approximations of the local Schur complements. For this, a symmetric singular value decomposition of a complex symmetric matix is used. Using the example of Maxwells equations the generality of the approach is demonstrated.
- ItemImproved dual meshes using Hodge-optimized triangulations for electromagnetic problems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Schlundt, RainerHodge-optimized triangulations (HOT) can optimize the dual mesh alone or both the primal and dual meshes. They make them more self-centered while keeping the primal-dual orthogonality. The weights are optimized in order to improve one or more of the discrete Hodge stars. Using the example of Maxwells equations we consider academic examples to demonstrate the generality of the approach.
- ItemShifted linear systems in electromagnetics : part 1: Systems with intentical right-hand sides(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Schlundt, Rainer; Schmückle, Franz-Josef; Heinrich, WolfgangWe consider the solution of multiply shifted linear systems for a single right-hand side. The coefficient matrix is symmetric, complex, and indefinite. The matrix is shifted by different multiples of the identity. Such problems arise in a number of applications, including the electromagnetic simulation in the development of microwave and mm-wave circuits and modules. The properties of microwave circuits can be described in terms of their scattering matrix which is extracted from the orthogonal decomposition of the electric field. We discretize the Maxwell's equations with orthogonal grids using the Finite Integration Technique (FIT). Some Krylov subspace methods have been used to solve multiply shifted systems for about the cost of solving just one system. We use the QMR method based on coupled two-term recurrences with polynomial preconditioning.
- ItemRegular triangulation and power diagrams for Maxwell's equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Schlundt, RainerWe consider the solution of electromagnetic problems. A mainly orthogonal and locally barycentric dual mesh is used to discretize the Maxwell's equations using the Finite Integration Technique (FIT). The use of weighted duals allows greater flexibility in the location of dual vertices keeping the primal-dual orthogonality. The construction of the constitutive matrices is performed using either discrete Hodge stars or microcells. Hodge-optimized triangulations (HOT) can optimize the dual mesh alone to make it more self-centered while maintaining the primal-dual orthogonality, e.g., the weights are optimized in order to improve one or more of the discrete Hodge stars.