A localised multiscale technique in boundary element method for acoustic wave model

The classical boundary element method (BEM) has emerged as a powerful alternative to the finite element method particularly in cases where better accuracy is required due to problems such as stress concentration or where the domain extends to infinity. In numerical calculation, the BEM has been widely used to solve acoustic problems since BEM offers excellent accuracy due to the discretization only on the structure's boundaries and easy mesh generation. However, BEM has some disadvantages. It suffers from certain drawbacks in terms of computational efficiency. Since most of the BEM leads to a linear system of equations with dense coefficient matrix, this prevents the BEM from being applied to large-scale problems or highresolution mesh. Due to these disadvantages, according to the acknowledged literature, some researchers use hybrid BEM coupling with other methods to improve the computational efficiency or to improve the computational time. This research uses a different technique from the existing hybrid BEM which will improve both the computational efficiency and time. This study highlights that BEM is less accurate for high gradient problem and consumes more computational time. To overcome this problem, a new technique known as multiscale boundary element method (MBEM) is introduced for solving two dimensional acoustic problems. MBEM is introduced in order to reduce the computation time and improve numerical accuracy using the localised multiscale boundary element method (LMBEM) with the help of the FORTRAN language and parallel routine OpenMP. In addition, the truncated Newton method and Newton interpolation are introduced in this multiscale technique. The multiscale technique produces the results faster because of interpolation and accurate initial guess value in a linear system while the mesh refinement for particular elements based on gradient produces more accurate results. Numerical calculation is given to illustrate the efficiency of the proposed method and the solutions have been validated and compared with the BEM. The results show that the MBEM is indeed faster than BEM, with the computational time reduction is almost 33.01%. When the 38 elements are solved using LMBEM, it is more accurate as it gives an average error that is almost similar to a ratio of 38:36 with the 1024 elements using MBEM and BEM. In addition, this research is solving the problem on the boundary. It is suggested that the current study be expanded to solve the problem for the internal nodes of the domain since the internal node value is needed

Preconditioning for time-harmonic Maxwell's equations using the Laguerre transform

A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential equations. However, solving large systems of linear algebraic equations with indefinite ill-conditioned matrices is a challenge. The high order of the matrices limits the capabilities of the Gaussian method to solve such systems, since this requires large RAM and much calculation. To reduce these requirements, an iterative preconditioned algorithm based on integral Laguerre transform in time is used. This approach allows using multigrid algorithms and, as a result, needs less RAM compared to the direct methods of solving systems of linear algebraic equations.Comment: 12 pages, 4 figure