PDE Timing, discrete vs FEM
Numerical solution of Partial Differential Equations, PDE, can be solved by various methods. One of the most common is Finite Element Method, FEM. Yet, the discrete method is similarly accurate and much faster. (Except on very small PDE's)
The following test runs use all possible terms and all possible derivatives. Thorough testing of software is very important to this software developer.Discrete Method second order in 2,3,4 dimensions
pde22js_eq.java pde22js_eq_java.out pde23js_eq.java pde23js_eq_java.out pde24js_eq.java pde24js_eq_java.outFinite Element Method second order in 2,3,4 dimensions
pde22js_la.java pde22js_la_java.out pde23js_la.java pde23js_la_java.out pde24js_la.java pde24js_la_java.outUtility files needed for discrete method
compute discrete derivative functions nuderiv.java solve simultaneous equations simeq.javaUtility files needed for finite element method
compute Phi functions laphi.java Gauss Legendre integration functions gaulegf.java solve simultaneous equations simeq.java seconds time maximum error pde22js_eq.java 0.12 1.2E-6 discrete pde23js_eq.java 0.12 1.8E-11 pde24js_eq.java 0.47 1.6E-9 pde22js_la.java 0.14 1.9E-14 FEM pde23js_la.java 34. 8.0E-10 pde24js_la.java 755. 1.6E-12 Faster algorithms are of interest