Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations

2007-12-10
Ozgun, Ozlem
Kuzuoğlu, Mustafa
In the numerical solution of some boundary value problems by the finite element method (FEM), the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain. The perfectly matched layer (PML) approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence. In this paper, we present the near-field numerical performance analysis of our new PML approach, which we call as locally-conformal PML, using Monte Carlo simulations. The locally-conformal PML method is ail easily implementable conformal PML implementation, to the problem of mesh truncation in the FEM. The most distinguished feature of the method is its simplicity and flexibility to design conformal PMLs over challenging geometries, especially those with curvature discontinuities, in a straightforward way without using artificial absorbers. The method is based on a special complex coordinate transformation which is 'locally-defined' for each point inside the PML region. The method can be implemented in an existing FEM software by just replacing the nodal coordinates inside the PM L region by their complex counterparts obtained via complex coordinate transformation. We first introduce the analytical derivation of the locally-conformal PML method for the FEM solution of the two-dimensional scalar Helmholtz equation arising in the mathematical modeling of various steadystate (or, time-harmonic) wave phenomena. Then, we carry out its numerical performance analysis by means of some Monte Carlo simulations which consider both the problem of constructing the two-dimensional Green's function, and some specific cases of electromagnetic scattering.
JOURNAL OF COMPUTATIONAL PHYSICS

Suggestions

On the use of complex stretching coordinates in generalized finite difference method with applications in inhomogeneous visco-elasto dynamics
Korkut, Fuat; Mengi, Yalcin; Tokdemir, Turgut (2022-01-01)
In the study, in conjunction with perfectly matched layer (PML) analysis, an approach is proposed for the evaluation of complex derivatives directly in terms of complex stretching coordinates of points in PML. For doing this within the framework of generalized finite difference method (GFDM), a difference equation is formulated and presented, where both the function values and coordinates of data points might be complex. The use of the proposed approach is considered in the analysis of inhomogeneous visco-e...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems
Bozkaya, Canan (2005-03-18)
The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Conformal perfectly matched absorbers in finite element mesh truncation
Kuzuoğlu, Mustafa; Mittra, R (2000-07-21)
In the numerical solution of electromagnetic scattering and/or radiation problems by finite methods, a mesh truncation scheme must be employed in order to obtain a bounded computational domain. We discuss the realization of perfectly matched absorbers by means of a complex coordinate transformation in a general coordinate system. In this way, it is possible to design perfectly matched layers (PMLs) which are conformal to the antenna/scatterer surface. The performance of the PMLs are tested for certain probl...
Least-squares finite element solution of Euler equations with adaptive mesh refinement
Akargün, Hayri Yiğit; Sert, Cüneyt; Department of Mechanical Engineering (2012)
Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the me...
FINITE DIFFERENCE APPROXIMATIONS OF VARIOUS STEKLOV EIGENVALUE PROBLEMS
ÖZALP, MÜCAHİT; Bozkaya, Canan; Türk, Önder; Department of Mathematics (2022-8-26)
In this thesis, the finite difference method (FDM) is employed to numerically solve differently defined Steklov eigenvalue problems (EVPs) that are characterized by the existence of a spectral parameter on the whole or a part of the domain boundary. The FDM approximation of the Laplace EVP is also considered due to the fact that the defining differential operator in a Steklov EVP is the Laplace operator. The fundamentals of FDM are covered and their applications on some BVPs involving Laplace operator are d...
Citation Formats
O. Ozgun and M. Kuzuoğlu, “Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations,” JOURNAL OF COMPUTATIONAL PHYSICS, pp. 1225–1245, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47399.