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UMBC High Performance Computing Facility
Highly Parallel Numerical Solution of Fourth Order Partial Differential Equations in 7 or more dimensions, with visualization of solution
Dr. Jon Squire, Computer Science and Electrical Engineering Department

With 10 grid points in each dimension, a PDE with 7 dimensions needs to solve 10^7 equations in 10^7 unknowns. This requires many parallel processors and much memory, and often high precision arithmetic. Then, displaying the results requires specialized software to visualize to solution. The modeling and simulation problems come from the bi-harmonic PDE applied to complex multi dimensional systems.