A Multithreaded Java Framework for Solving Linear Elliptic Partial Differential Equations in 3D

Our research in theoretical biophysics [6] recently required us to solve a variant of the Poisson equation, which is a linear elliptic partial differential equation (PDE) in 3D. Ultimately, we want to make our method available as a applet, so we decided to implement a PDE solver in Java. Another reason for using Java was its promise of easy, portable multithreaded programming, because support for multithreading is built into Java. On a Symmetric Multi-Processor (SMP) this offers the opportunity to painlessly achieve parallel execution, which might be important for the numerically intensive (though certainly not excessive) task of solving a PDE. The Java framework described here allows the solution of any linear elliptic PDE on a regular cubic domain in 3D. To this end it employs the Full Multigrid (FMG) algorithm [3, 1, 7], which is the most efficient general-purpose algorithm widely used for this problem domain. The framework is easily extensible in every aspect of the PDE algorithm and was designed with interactive Java applets in mind. The framework is implemented in the 1.1 release of Java.