A new family of mixed finite elements in IR3
Numerische Mathematik
Journal of Computational and Applied Mathematics
Two polynomial methods of calculating functions of symmetric matrices
USSR Computational Mathematics and Mathematical Physics
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Calculation of functions of unsymmetric matrices using Arnoldi's method
Computational Mathematics and Mathematical Physics
A dispersion analysis of finite element methods for Maxwell's equations
SIAM Journal on Scientific Computing
Explicit Runge-Kutta methods for parabolic partial differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Matrix computations (3rd ed.)
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
SIAM Journal on Matrix Analysis and Applications
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
Stability control for approximate implicit time stepping schemes with minimum residual iterations
Applied Numerical Mathematics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Preconditioning Lanczos Approximations to the Matrix Exponential
SIAM Journal on Scientific Computing
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Application of operator splitting to the Maxwell equations including a source term
Applied Numerical Mathematics
Hi-index | 31.45 |
For the time integration of edge finite element discretizations of the three-dimensional Maxwell equations, we consider the Gautschi cosine scheme where the action of the matrix function is approximated by a Krylov subspace method. First, for the space-discretized edge finite element Maxwell equations, the dispersion error of this scheme is analyzed in detail and compared to that of two conventional schemes. Second, we show that the scheme can be implemented in such a way that a higher accuracy can be achieved within less computational time (as compared to other implicit schemes). We also analyzed the error made in the Krylov subspace matrix function evaluations. Although the new scheme is unconditionally stable, it is explicit in structure: as an explicit scheme, it requires only the solution of linear systems with the mass matrix.