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

In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system of equations describing the circuit (Modified Nodal Analysis) which yields a system of Differential Algebraic Equations (DAEs). This paper deals with the differential index analysis of such coupled systems. For that, a new generalised inductance-like element is defined. The index of the DAEs obtained from a circuit containing such an element is then related to the topological characteristics of the circuit's underlying graph. Field/circuit coupling is performed when circuits are simulated containing elements described by Maxwell's equations. The index of such systems with two different types of magnetoquasistatic formulations (A* and T-$\Omega$) is then deduced by showing that the spatial discretisations in both cases lead to an inductance-like element.

A Structural Analysis of Field/Circuit Coupled Problems Based on a Generalised Circuit Element

In the design of electromagnetic devices the accurate representation of the geometry plays a crucial role in determining the device performance. For accelerator cavities, in particular, controlling the frequencies of the eigenmodes is important in order to guarantee the synchronization between the electromagnetic field and the accelerated particles. The main interest of this work is in the evaluation of eigenmode sensitivities with respect to geometrical changes using Monte Carlo simulations and stochastic collocation. The choice of an Isogeometric Analysis approach for the spatial discretization allows for an exact handling of the geometrical domains and their deformations, guaranteeing, at the same time, accurate and highly regular solutions.

Isogeometric Analysis simulation of TESLA cavities under uncertainty

In this paper, the concept of multirate partial differential equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The MPDEs are solved by a Galerkin approach and a conventional time discretization. Nonlinearities are efficiently accounted for by neglecting the high-frequency components (ripples) of the state variables and using only their envelope for the evaluation. It is shown that the impact of this approximation on the solution becomes increasingly negligible for rising frequency and leads to significant performance gains.

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Solving Nonlinear Circuits With Pulsed Excitation by Multirate Partial Differential Equations

The Parareal algorithm allows one to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We ...

A New Parareal Algorithm for Problems with Discontinuous Sources

In this paper domain substructuring is adapted to the nonlinear transient eddy current problem: conductive and nonconductive domains are separately treated for a more efficient time integration. A matrix factorization of the linear (nonconductive) subproblem, e.g., air, is executed on beforehand and used throughout the simulation. For a general 3D problem these non-sparse factors must be replaced by sparse approximations or explicit time integration must be carried out to increase the efficiency of the solution process. This approach is validated using implicit and half-explicit time integration methods. Numerical results underline the feasibility and the possible gain obtained by higher order half-explicit methods.

Sebastian Schöps

Papers

A Structural Analysis of Field/Circuit Coupled Problems Based on a Generalised Circuit Element

Isogeometric Analysis simulation of TESLA cavities under uncertainty

Solving Nonlinear Circuits With Pulsed Excitation by Multirate Partial Differential Equations

A New Parareal Algorithm for Problems with Discontinuous Sources

Higher Order Half-Explicit Time Integration of Eddy Current Problems Using Domain Substructuring