Kazuki Niino

A discretisation method with a H div scalar product for boudnary integra equation methods

A new discretisation method with a Hdiv scalar product for boundary element methods is proposed. This method improves the accuracy of boundary element methods for the PMCHWT formulations for Maxwells equations. In particular, this method is effective for low-frequency problems in which conventional methods suffer from bad accuracy. We verify the efficiency of this method through some numerical examples.

A novel preconditioner for the EFIE discretised with the H div inner product

A novel preconditioning for the electric field integral equation (EFIE) discretised with the Hdiv inner product is discussed. It is known that the EFIE suffers from bad accuracy in low-frequency problems. One of the remedies for this bad accuracy is the discretisation method using Hdiv inner product. The EFIE with this discretisation, however, shows slow convergence of iteration methods and, what is worse, a naive application of the Calderon preconditioning is not effective for accelerating the convergence. In this paper, we will propose a new preconditioning, which can efficiently reduce the computational time of the EFIE discretised with the Hdiv inner product.

Boundary Integral Equations for Calculating Complex Eigenvalues of Transmission Problems

Resonance frequencies are complex eigenvalues at which the homogeneous transmission problems have nontrivial solutions. These frequencies are of interest because they affect the behavior of the solutions even when the frequency is real. The resonance frequencies are related to problems for infinite domains which can be solved efficiently with the boundary integral equation method (BIEM). We thus consider a numerical method for determining resonance frequencies with fast BIEM and the Sakurai--Sugiura projection method. However, BIEM may have fictitious eigenvalues even when one uses Muller or PMCHWT formulations which are known to be resonance free when the frequency is real valued. In this paper, we propose new BIEs for transmission problems with which one can distinguish true and fictitious eigenvalues easily. Specifically, we consider waveguide problems for the Helmholtz equation in two dimensions and standard scattering problems for Maxwells equations in three dimensions. We verify numerically that th...

On the BEMs with the Müller formulation and the Nyström method for periodic electromagnetic scattering problems

We investigate a boundary element method with Müllers formulation for dielectric scattering problems in periodic domains. In this method, the iteration number of iterative methods is expected to be small since the operators in Müllers formulation are essentially identical with the unit operator to within a compact operator. We use the Nyström method for the discretisation so that we do not need to use any basis functions. We make several numerical experiments to see the accuracy and the efficiency of this method.

New preconditioning methods based on Calderón's formulae for PMCHWT formulation

Preconditioning methods based on Calderóns formulae for PMCHWT formulations for Maxwells equations in 3D are discussed. We propose two preconditioning methods which use different basis functions for surface electric and magnetic currents. The first method is a preconditioning just by appropriately ordering the coefficient matrix and using the Grammian matrix as the preconditioner. The second type utilises preconditioners constructed by using matrices needed in the main FMM algorithms. We will show through several numerical examples that these two preconditioning methods are faster than conventional methods.