Waveform relaxation: a convergence criterion for differential-algebraic equations

被引:4
|
作者
Pade, Jonas [1 ]
Tischendorf, Caren [1 ]
机构
[1] Humboldt Univ, Dept Math, Rudower Chaussee 25 Johann von Neumann Haus, D-12489 Berlin, Germany
关键词
Differential-algebraic equation; DAE; Waveform relaxation; Dynamic iteration; Cosimulation; Electrical circuit; Network topology; Convergence; DYNAMIC ITERATION;
D O I
10.1007/s11075-018-0645-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
While waveform relaxation (also known as dynamic iteration or co-simulation) methods are known to converge for coupled systems of ordinary differential equations (ODEs), they may suffer from instabilities for coupled differential-algebraic equations (DAEs). Several convergence criteria have been developed for index-1 DAEs. We present here a convergence criterion for a coupled system of an index-2 DAE with an ODE. The analysis is motivated by the wish to combine electromagnetic field simulation with circuit simulation in a stable manner. The spatially discretized Maxwell equations in vector potential formulation with Lorenz gauging represent an ODE system. A lumped circuit model via the established modified nodal analysis is known to be a DAE system of index <= 2. Finally, we present sufficient network topological criteria to the coupling that are easy to check and that guarantee convergence.
引用
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页码:1327 / 1342
页数:16
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