Advanced Numerical Methods in the Mathematical Sciences

• May 4–7, 2015
• Texas A&M University
• College Station, TX
• Rudder Tower (RDER) 501

Myoungnyoun Kim, National Institute for Mathematical Sciences (South Korea)

Multilevel Monte Carlo Method for the Helmholtz Equation with Random Coefficients

Authors

• Myoungnyoun Kim, National Institute for Mathematical Sciences (South Korea)
• Imbo Sim, National Institute for Mathematical Sciences (South Korea)

Abstract

We apply the multilevel Monte Carlo method to Helmholtz equation with random coefficients. A variant of the multilevel Monte Carlo method is designed from the consideration of the Krigging method between the consecutive levels and applied to the same problem to test its efficiency and convergence. The main feature of the multilevel Monte Carlo method is the smaller number of samples than that of the usual Monte Carlo method, which is kept in the new method. Computational savings are predicted and observed during the test. We demonstrate the cost and convergence of our method.