Sergey Polstyanko

Fast frequency sweep technique for the efficient analysis of dielectric waveguides

This paper describes a new approach to spectral response computations of an arbitrary two-dimensional (2-D) waveguide. This technique is based on the tangential-vector finite-element method (TVFEM) in conjunction with the asymptotic waveform evaluation (AWE) technique. The former is used to obtain modes characteristics for a central frequency, whereas the latter employs an efficient algorithm to compute frequency moments for each mode. These moments are then matched via Pade approximation to a reduced-order rational polynomial, which can be used to interpolate each mode over a frequency band with a high degree of accuracy. Furthermore, the moments computations and subsequent interpolation for a given set of frequency points can be done much more rapidly than just simple simulations for each frequency point.

Application of anisotropic absorbers to the analysis of MMIC devices by the finite element method

Anisotropic material characteristics can be exploited to construct absorbers that provide reflectionless interfaces for waves at arbitrary incident angles. Since their computer implementation requires the specification of appropriate material characteristics only, these perfectly matched layers (PMLs) allow for simple but accurate mesh truncation schemes for the finite element method. The present paper extends the concept of PMLs to waveguides of inhomogeneous cross-sections and layered media. We describe the use of generalized PMLs in a software package for (M)MIC devices and demonstrate the benefits of the suggested approach by two numerical examples.

Algebraic multigrid method for solving FEM matrix equations for 3D static problems

An implementation of the algebraic multigrid method and its application for solving matrix equations arising from 3D FEM static analysis are addressed. The method, which is based on multigrid principles, is designed to solve such problems efficiently by using only the information contained in the matrix equation itself without any geometrical background. A number of numerical experiments have been conducted to study the complexity of the algorithm as well as its convergence behavior.

Power Aware Parallel 3-D Finite Element Mesh Refinement Performance Modeling and Analysis With CUDA/MPI on GPU and Multi-Core Architecture

Software power performance tuning handles the critical design constraints of software running on hardware platforms composed of large numbers of power-hungry components. The power dissipation of a Single Program/Instruction Multiple Data (SPMD/SIMD) computation such as finite element method (FEM) mesh refinement is highly dependent on the underlying algorithm and the power-consuming features of hardware Processing Elements (PE). This contribution presents a practical methodology for modeling and analyzing the power performance of parallel 3-D FEM mesh refinement on CUDA/MPI architecture based on detailed software prototypes and power parameters in order to predict the power functionality and runtime behavior of the algorithm, optimize the program design and thus achieve the best power efficiency. In detail, we have proposed approaches for GPU parallelization, dynamic CPU frequency scaling and dynamic load scheduling among PEs. The performance improvement of our designs has been demonstrated and the results have been validated on a real multi-core and GPU cluster.

Adaptive finite element electrostatic solver

A new adaptive h-version finite element algorithm is presented and its performance is compared with uniform h- and p-versions of the finite element analysis. It is shown that the adaptive strategy allows considerable improvement in the overall efficiency and performance of the solution process with respect to the solution accuracy and computational time.

Coupled thermal-fluid-electrical simulation for printed circuit board design

In this work we describe a coupled thermal-fluid-electrical simulation for printed circuit boards and their surrounding enclosures. A finite-element based electrical solver is used to compute the distribution of electrical currents and ohmic power losses in the boards power and ground distribution network. The power loss information is then used as an input to a computational fluid dynamics (CFD) solver. The CFD solver computes the resulting air flow velocities and temperature distribution in the board and its surroundings. The temperature map is then returned to the electrical solver, which adjusts the electrical conductivity as a function of position and computes an updated set of current and power losses. This procedure is iterated until it obtains a converged, self-consistent solution for the steady-state temperature and ohmic power loss distributions in the board-enclosure system.

Full wave vector Maxwell equation simulation of nonlinear self-focusing effects in three spatial dimensions

In our effort to meet an increasing demand for more accurate and realistic nonlinear optics simulations, we have developed a nonlinear hybrid vector finite element method (NL-HVFEM) to study different phenomena due to wave propagation in waveguides filled with nonlinear Kerr-type media. Contrary to the most existing scalar models, the NL-HVFEM approach is based upon the vector Helmholtz equation and thus can predict the vectorial properties of fields in nonlinear media. We describe the NL-HVFEM approach and apply it to study nonlinear self-focusing effects in nonlinear waveguides. The numerical results of the evolution of the beam self-focusing are also included. Also, we summarized conditions under which electromagnetic beam can produce its own dielectric waveguide and propagate without spreading.

A novel Modal and Domain Decomposition method for printed Circuit Boards and packages

The paper presents a novel Modal and Domain Decomposition approach for fast and accurate analysis of high-speed Printed Circuit Boards (PCBs) and electronic packages. This combined method overcomes both the accuracy limitations of the classic Modal Decomposition Method and the significant performance limitations encountered with any 3D full-wave method. The proposed combined method utilizes an Integral Equation (IE)-based solver for critical 3D regions. The IE solver and the Modal Decomposition solver, which is based on the 2D Finite Element Method (FEM), are seamlessly connected through the admittance matrix at the domain boundary. The accuracy and efficiency of this pioneering method has been verified through an example.

Parallel processing improvements for full-wave electromagnetic solvers

As computing resources become increasingly parallel for both shared and distributed memory systems, computational electromagnetic methods need to take full advantage of new architectures in order to reduce simulation times. Several different aspects of the solution process make it difficult for traditional finite element field solvers to effectively utilize distributed and shared memory resources. This paper will provide insight into recent advancements made in the finite element method matrix solve (shared memory) and frequency sweep (distributed memory) that drastically reduce simulation times for signal and power integrity applications.

Fast Schwarz-type finite element electrostatic solver

A new p-type finite element solver is presented for the efficient solution of 3D electrostatic problems. Its efficiency comes from a careful implementation of multigrid ideas within the finite element framework. A multigrid-type preconditioner is developed for the Conjugate Gradient method, which leads to the overall O(N/sup 1.1/) complexity.