FEYNMAN_KAC_3D
PDE Solution by Feynman-Kac Algorithm

FEYNMAN_KAC_3D is a C++ program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson's equation in a 3D ellipsoid by averaging stochastic paths to the boundary.

The program is intended as a simple demonstration of the method. The main purpose is to have a version that runs sequentially, so that it can be compared to versions which have been enhanced using parallel programming techniques.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

FEYNMAN_KAC_3D is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEYNMAN_KAC_1D, a C++ program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson's equation in a 1D interval by averaging stochastic paths to the boundary.

FEYNMAN_KAC_2D, a C++ program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson's equation in a 2D ellipse by averaging stochastic paths to the boundary.

SDE, a MATLAB library which solves certain stochastic differential equations.

STOCHASTIC_RK, a C++ library which applies a Runge-Kutta scheme to a stochastic differential equation.

Reference:

1. Peter Arbenz, Wesley Petersen,
   Introduction to Parallel Computing - A practical guide with examples in C,
   Oxford University Press,
   ISBN: 0-19-851576-6,
   LC: QA76.58.P47.

Source Code:

• feynman_kac_3d.cpp, the source code.
• feynman_kac_3d.sh, commands to compile and load the source code.

Examples and Tests:

• feynman_kac_3d_output.txt, the output file.

List of Routines:

• MAIN is the main program for FEYNMAN_KAC_3D.
• POTENTIAL evaluates the potential function V(X,Y,Z).
• R8_ABS returns the absolute value of an R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.