Universal modification of vector weighted method of dependent trials

Abstract

Vector weighted Monte Carlo algorithms for the estimation of linear functionals of set of solutions of systems of the 2nd kind integral equations are studied. A universal modification of the vector weighted method of dependent trials with branching of the Markov chain trajectory relative to the elements of matrix weight is constructed. It is shown that the computational cost of the constructed algorithms is finite in the case when the solutions of systems of the 2nd kind are bounded. The application of constructed method of dependent trials is presented for some problems of the radiation transfer theory with allowance for polarization and multigroup transport theory.

Keywords:

• System of linear integral equations
• Vector weight estimator
• Matrix weight
• Weighted method of dependent trials
• Branching of Markov chain trajectory
• Computation cost
• Transfer of polarized radiation
• Multigroup transport theory

Additional information

Funding

The reported study was funded by RFBR according to the research projects 18-01-00356 and 17-01-00823.