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Published in:
2012 | OriginalPaper | Chapter
Effective Numerical Computation of Parameter Dependent Problems
Authors : Lennart Jansen, Caren Tischendorf
Published in: Scientific Computing in Electrical Engineering SCEE 2010
Publisher: Springer Berlin Heidelberg
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We analyse parameter dependent differential-algebraic-equations (DAEs)
$$Ad\prime(x,t,p) + b(x,t,p) = 0.$$
For these systems one is interested in the relation between the numerical solutions
x
and some associated parameters
p
. The standard approach is to discretise the equations with respect to the parameters and solve the parameter independent equations afterwards. This approach forces a calculation of the differential equations multiple times (for a huge number of parameter values
p
). This may lead to high computational costs. By using the already computed solutions to calculate the remaining ones and thus exploiting the smoothness of the solution with respect to the parameters, it is possible to save the majority of the computational cost.