A space mapping approach for the p-Laplace equation

Motivated by car safety applications the goal is to deternmine a thickness coefficient in the nonlinear p-Laplace equation. The associated optimal problem is hard to solve numerically. Therefore, the computationally expensive, nonlinear p-Laplace equation is replaced by a simpler, linear model. The space mapping technique is utilized to link the linear and nonlinear equations and drives the optimization iteration of the time intensive nonlinear equation using the fast linear equation.For this reason an efficient realization of the space mapping is utilized. Numerical examples are presented to illustrate the advantage of the proposed approach.

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