GMGS-3D

A Geometric Multigrid Solver for Large-scale Static Finite Element Simulation on 3D Cartesian Mesh

# Target
Out of academic use, "GMGS-3D" is designed to generate the high-resolution data sets of vector (displacement) or
2nd-order tensor (stress) field with the NORMAL PC within an AFFORDABLE time.

# Design description
"GMGS-3D" proceeds the static Finite Element Analysis (FEA) for solid objects discretized into Cartesian mesh, where,
1) an element index based data structure is used to store the FEA stiffness matrix;
2) combined with the Jacobian smoother, a Geometric Multigrid based V-cycle is built on the Cartesian mesh;
3) the FEA equation is iteratively solved by Conjugate Gradient Method preconditioned with V-cycle;
4) besides the displacement vector field, the stress tensor field also can be computed.

# Limitations
Geometric Multigrid method can go well with some hardware accelerating techniques, yet in this program, the author didn't
look much into it, given his limited experience in that area, and the specific design target. Any suggestions about improving
performance are highly welcomed.

# Statistics
Experiment Environment: A desktop equipped with Intel(@) Core i7-7700k and 32GB RAM, convergence tolerance = 1.0e-3

# Example 1: kitten
Resolutions DOFs Time Costs (s)
42x37x64 120,198 1.49
84x73x128 929,961 20.7
169x147x256 6,732,912 349
337x294x512 52,499,889 4030
428x373x650 106,873,614 8200
# Example 2: parts
Resolutions DOFs Time Costs (s)
46x46x64 141,744 2.74
91x91x128 999,342 56.1
183x183x256 7,570,380 208
366x366x512 58,608,732 2850
464x464x650 118,761,510 5330