Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic Problems

This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton--Raphson scheme. The resolution of many mesoscale problems per Gauss point allows to compute the homogenized constitutive law and its derivative by finite differences. In the proposed approach, the macroscale problem and the mesoscale problems are weakly coupled and solved separately using the finite element method on time intervals for several waveform relaxation iterations. The exchange of information between both problems is still carried out using the heterogeneous multiscale method. However, the partial derivatives can now be evaluated exactly by solving only one mesoscale problem per Gauss point.Comment: submitted to JC

Circuit simulation using distributed waveform relaxation techniques

Simulation plays an important role in the design of integrated circuits. Due to high costs and large delays involved in their fabrication, simulation is commonly used to verify functionality and to predict performance before fabrication. This thesis describes analysis, implementation and performance evaluation of a distributed memory parallel waveform relaxation technique for the electrical circuit simulation of MOS VLSI circuits. The waveform relaxation technique exhibits inherent parallelism due to the partitioning of a circuit into a number of sub-circuits. These subcircuits can be concurrently simulated on parallel processors. Different forms of parallelism in the direct method and the waveform relaxation technique are studied. An analysis of single queue and distributed queue approaches to implement parallel waveform relaxation on distributed memory machines is performed and their performance implications are studied. The distributed queue approach selected for exploiting the coarse grain parallelism across sub-circuits is described. Parallel waveform relaxation programs based on Gauss-Seidel and Gauss-Jacobi techniques are implemented using a network of eight Transputers. Static and dynamic load balancing strategies are studied. A dynamic load balancing algorithm is developed and implemented. Results of parallel implementation are analyzed to identify sources of bottlenecks. This thesis has demonstrated the applicability of a low cost distributed memory multi-computer system for simulation of MOS VLSI circuits. Speed-up measurements prove that a five times improvement in the speed of calculations can be achieved using a full window parallel Gauss-Jacobi waveform relaxation algorithm. Analysis of overheads shows that load imbalance is the major source of overhead and that the fraction of the computation which must be performed sequentially is very low. Communication overhead depends on the nature of the parallel architecture and the design of communication mechanisms. The run-time environment (parallel processing framework) developed in this research exploits features of the Transputer architecture to reduce the effect of the communication overhead by effectively overlapping computation with communications, and running communications processes at a higher priority. This research will contribute to the development of low cost, high performance workstations for computer-aided design and analysis of VLSI circuits

The Parallel Implementation of the Waveform Relaxation Method for Transient Stability Simulations

In this paper, the authors extend the results of their earlier paper on waveform relamtion (WR), which is a parallel algorithm for transient stability analysis. The WR algorithm is extended to a structure-preserving power system model in which the loads are retained. This results in a system of differential/ algebraic equations (DAEs). Power systems exhibit several unique dynamic properties which may be exploited in an advantageous manner by the WR algorithm. This leads to a greater computational efficiency than most other direct methods of simulation. This paper presents several theoretical results as well as computational results on parallel implementation

A Waveform Relaxation Solver for Transient Simulation of Large-Scale Nonlinearly Loaded Shielding Structures

This article introduces an algorithm for transient simulation of electromagnetic structures loaded by lumped nonlinear devices. The reference application is energy-selective shielding, which adopts clipping devices uniformly spread along shield apertures to achieve a shielding effectiveness that increases with the power of the incident field, thereby blocking high-power interference while allowing low-power communication. Transient simulation of such structures poses a number of challenges, related to their large-scale and low-loss nature. In this work, we propose a waveform relaxation (WR) scheme based on decoupling the linear electromagnetic structure from its nonlinear terminations. In a preprocessing stage, the electromagnetic subsystem is characterized in the frequency domain and converted into a behavioral rational macromodel. Transient simulation is performed by refining estimates of the port signals through iterations. The proposed scheme combines a time partitioning approach with an inexact Newton–Krylov solver. This combination provides fast convergence also in those cases where standard WR schemes fail due to a strong mismatch at the decoupling sections. Numerical results on several test cases of increasing complexity with up to 1024 ports show that the proposed approach proves as reliable as HSPICE in terms of accuracy, with a speedup ranging from one to three orders of magnitude

Custom Integrated Circuits

Contains reports on nine research projects.Analog Devices, Inc.International Business Machines CorporationJoint Services Electronics Program Contract DAAL03-89-C-0001U.S. Air Force - Office of Scientific Research Contract AFOSR 86-0164BDuPont CorporationNational Science Foundation Grant MIP 88-14612U.S. Navy - Office of Naval Research Contract N00014-87-K-0825American Telephone and TelegraphDigital Equipment CorporationNational Science Foundation Grant MIP 88-5876

Custom Integrated Circuits

Contains reports on twelve research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAAL03-86-K-0002)Joint Services Electronics Program (Contract DAAL03-89-C-0001)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI Semiconductor, Inc.U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryNational Science Foundation (Grant MIP 84-07285)National Science Foundation (Grant MIP 87-14969)Battelle LaboratoriesNational Science Foundation (Grant MIP 88-14612)DuPont CorporationDefense Advanced Research Projects Agency/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)American Telephone and TelegraphDigital Equipment CorporationNational Science Foundation (Grant MIP-88-58764

Custom Integrated Circuits

Contains reports on nine research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAALO03-86-K-0002)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI SemiconductorU.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryDARPA/U.S. Navy - Office of Naval Research (Contract N00014-80-C-0622)DARPA/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)National Science Foundation (Grant ECS-83-10941)AT&T Bell Laboratorie

Custom Integrated Circuits

Contains reports on ten research projects.Analog Devices, Inc.IBM CorporationNational Science Foundation/Defense Advanced Research Projects Agency Grant MIP 88-14612Analog Devices Career Development Assistant ProfessorshipU.S. Navy - Office of Naval Research Contract N0014-87-K-0825AT&TDigital Equipment CorporationNational Science Foundation Grant MIP 88-5876