Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

An introduction to heat transfer

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Introduction To Electrodynamics

Finite element methods for Maxwell's equations.

Introduction to heat transfer

Purpose – The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation. Design/methodology/approach – The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis. Findings – This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation. Originality/value – The presentat...

Winding functions in transient magnetoquasistatic field-circuit coupled simulations

This paper proposes a framework of waveform relaxation methods to simulate electromagnetic fields coupled to electric networks. Within this framework, a guarantee for convergence and stability of Gaus-Seidel-type methods is found by partial differential algebraic equation (PDAE) analysis. It is shown that different time step sizes in different parts of the model can be automatically chosen according to the problem's dynamics. A finite-element model of a transformer coupled to a circuit illustrates the efficiency of multirate methods.

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A Cosimulation Framework for Multirate Time Integration of Field/Circuit Coupled Problems

Coupled systems of differential-algebraic equations (DAEs) may suffer from instabilities during a dynamic iteration We extend the existing analysis on recursion estimates, error propagation, and stability to (semiexplicit) index-1 DAEs In this context, we discuss the influence of certain coupling structures and the computational sequence of the subsystems on the rate of convergence Furthermore, we investigate in detail convergence and divergence for two coupled problems stemming from refined electric circuit simulation These are the semiconductor-circuit and field-circuit couplings We quantify the convergence rate and behavior also using Lipschitz constants and suggest an enhanced modeling of the coupling interface in order to improve convergence

Dynamic Iteration for Coupled Problems of Electric Circuits and Distributed Devices

A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

http://www2.math.uni-wuppertal.de/opt/preprints/prep2010/amna_opap_10_10.pdf

Sebastian Schöps

Papers

Winding functions in transient magnetoquasistatic field-circuit coupled simulations

A Cosimulation Framework for Multirate Time Integration of Field/Circuit Coupled Problems

Dynamic Iteration for Coupled Problems of Electric Circuits and Distributed Devices

A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

Structural analysis of electrical circuits including magnetoquasistatic devices