Paper 29

Generated: Mon Aug 29 11:01:18 2011

29 - Title Parallelization of a Fokker-Planck approximation of the master equation
Authors Paul Sjöberg, Scientific Computing/Dept of Information tech, Uppsala University
Contact person Paul Sjöberg
Main Fields 3. Biology
7. Computational Science
Abstract + Keywords Stochastical models of molecular control systems give rise to master equations. The master equation describe the probability of being in the different states of the system, and the solution to the equation is a probability denisity function of the state space.

Each molecular species that are included in the model adds a dimension to the problem. Analytical solutions are possible only for simple cases.
Even rather small models containing three or four species can will be computationally cumbersome.

The problem is usually solved using Monte Carlo simulations, but larger problems can be solved by using a Fokker-Planck (PDE) approximation of the master equation (ODE). The PDE allows a reduction of the nodes used to resolve the state space.

The subject for this project is to parallelize an existing program that generate the Fokker-Planck equation from a set of reaction rules (the molecular model). The output is used to solve the equation by implicit time stepping methods, preferredly implemented in software packages.

The program is written in C++ and is by no means serially optimized. Since the generation of the Fokker-Planck equation should be embaressingly parallel, serial optimization will be an important part of the project. The parallelization will be made in OpenMP and if time allows in MPI.
Remarks

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29 - Title	Parallelization of a Fokker-Planck approximation of the master equation
Authors	Paul Sjöberg, Scientific Computing/Dept of Information tech, Uppsala University
Contact person	Paul Sjöberg
Main Fields	3. Biology 7. Computational Science
Abstract + Keywords	Stochastical models of molecular control systems give rise to master equations. The master equation describe the probability of being in the different states of the system, and the solution to the equation is a probability denisity function of the state space. Each molecular species that are included in the model adds a dimension to the problem. Analytical solutions are possible only for simple cases. Even rather small models containing three or four species can will be computationally cumbersome. The problem is usually solved using Monte Carlo simulations, but larger problems can be solved by using a Fokker-Planck (PDE) approximation of the master equation (ODE). The PDE allows a reduction of the nodes used to resolve the state space. The subject for this project is to parallelize an existing program that generate the Fokker-Planck equation from a set of reaction rules (the molecular model). The output is used to solve the equation by implicit time stepping methods, preferredly implemented in software packages. The program is written in C++ and is by no means serially optimized. Since the generation of the Fokker-Planck equation should be embaressingly parallel, serial optimization will be an important part of the project. The parallelization will be made in OpenMP and if time allows in MPI.
Remarks