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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.