8,764 research outputs found
Transient Analysis of High-Speed Channels via Newton-GMRES Waveform Relaxation
This paper presents a technique for the numerical simulation of coupled high-speed channels terminated by arbitrary nonlinear drivers and receivers. The method builds on a number of existing techniques. A Delayed-Rational Macromodel is used to describe the channel in compact form, and a general Waveform Relaxation framework is used to cast the solution as an iterative process that refines initial estimates of transient scattering waves at the channel ports. Since a plain Waveform Relaxation approach is not able to guarantee convergence, we turn to a more general class of nonlinear algebraic solvers based on a combination of the Newton method with a Generalized Minimal Residual iteration, where the Waveform Relaxation equations act as a preconditioner. The convergence of this scheme can be proved in the general case. Numerical examples show that very few iterations are indeed required even for strongly nonlinear termination
Compressed Passive Macromodeling
This paper presents an approach for the extraction of passive macromodels of large-scale interconnects from their frequency-domain scattering responses. Here, large scale is intended both in terms of number of electrical ports and required dynamic model order. For such structures, standard approaches based on rational approximation via vector fitting and passivity enforcement via model perturbation may fail because of excessive computational requirements, both in terms of memory size and runtime. Our approach addresses this complexity by first reducing the redundancy in the raw scattering responses through a projection and approximation process based on a truncated singular value decomposition. Then we formulate a compressed rational fitting and passivity enforcement framework which is able to obtain speedup factors up to 2 and 3 orders of magnitude with respect to standard approaches, with full control over the approximation errors. Numerical results on a large set of benchmark cases demonstrate the effectiveness of the proposed techniqu
Application of the Waveform Relaxation Technique to the Co-Simulation of Power Converter Controller and Electrical Circuit Models
In this paper we present the co-simulation of a PID class power converter
controller and an electrical circuit by means of the waveform relaxation
technique. The simulation of the controller model is characterized by a
fixed-time stepping scheme reflecting its digital implementation, whereas a
circuit simulation usually employs an adaptive time stepping scheme in order to
account for a wide range of time constants within the circuit model. In order
to maintain the characteristic of both models as well as to facilitate model
replacement, we treat them separately by means of input/output relations and
propose an application of a waveform relaxation algorithm. Furthermore, the
maximum and minimum number of iterations of the proposed algorithm are
mathematically analyzed. The concept of controller/circuit coupling is
illustrated by an example of the co-simulation of a PI power converter
controller and a model of the main dipole circuit of the Large Hadron Collider
A Time-Dependent Dirichlet-Neumann Method for the Heat Equation
We present a waveform relaxation version of the Dirichlet-Neumann method for
parabolic problem. Like the Dirichlet-Neumann method for steady problems, the
method is based on a non-overlapping spatial domain decomposition, and the
iteration involves subdomain solves with Dirichlet boundary conditions followed
by subdomain solves with Neumann boundary conditions. However, each subdomain
problem is now in space and time, and the interface conditions are also
time-dependent. Using a Laplace transform argument, we show for the heat
equation that when we consider finite time intervals, the Dirichlet-Neumann
method converges, similar to the case of Schwarz waveform relaxation
algorithms. The convergence rate depends on the length of the subdomains as
well as the size of the time window. In this discussion, we only stick to the
linear bound. We illustrate our results with numerical experiments.Comment: 9 pages, 5 figures, Lecture Notes in Computational Science and
Engineering, Vol. 98, Springer-Verlag 201
Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation for the Wave Equation
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann and
Neumann-Neumann algorithms for the wave equation in space time. Each method is
based on a non-overlapping spatial domain decomposition, and the iteration
involves subdomain solves in space time with corresponding interface condition,
followed by a correction step. Using a Laplace transform argument, for a
particular relaxation parameter, we prove convergence of both algorithms in a
finite number of steps for finite time intervals. The number of steps depends
on the size of the subdomains and the time window length on which the
algorithms are employed. We illustrate the performance of the algorithms with
numerical results, and also show a comparison with classical and optimized
Schwarz WR methods.Comment: 8 pages, 6 figures, presented in 22nd International conference on
Domain Decomposition Methods, to appear in Domain Decomposition in Science
and Engineering XXII, LNCSE, Springer-Verlag 201
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
Pipeline Implementations of Neumann-Neumann and Dirichlet-Neumann Waveform Relaxation Methods
This paper is concerned with the reformulation of Neumann-Neumann Waveform
Relaxation (NNWR) methods and Dirichlet-Neumann Waveform Relaxation (DNWR)
methods, a family of parallel space-time approaches to solving time-dependent
PDEs. By changing the order of the operations, pipeline-parallel computation of
the waveform iterates are possible without changing the final solution. The
parallel efficiency and the increased communication cost of the pipeline
implementation is presented, along with weak scaling studies to show the
effectiveness of the pipeline NNWR and DNWR algorithms.Comment: 20 pages, 8 figure
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