galerkin / PainlessMG

PainlessMG

This code is developed base on Huaming Wang's code base http://web.cse.ohio-state.edu/~wang.3602/Wang-2015-ACS/Chebyshev_sim.zip

Usage

Codes in CUDA_Projective_Armadillo is for a tet mesh simulation.
Codes in CUDA_Projective_Square is for a mass-spring cloth simulation.

Settings of simulation can be hard coded. However to get rid of recompilation, we provide a way to load setting from files.

Format of the config file

For cloth simulations:

Overview

[cloth size]

[output directory of benckmark records]

[enable benchmark]

[number of iterations in one frame] [enable Hessian] [enable Chebyshev] [enable pre-factorization on the finest level]

[number of coarsened level]

[number of vertices in each coarsened level, begin from the coarsest level]

[save matrix in each level (including the finest level) in a dense matrix memory layout]

[save matrix in each level (including the finest level) in a LDU memory layout]

[number of multigrid operations]

[list of multigrid operations]

[parameter for Chebyshev]

[number of objects in the scene]

[list of objects in the scene]

Detail Explaination

cloth size:
number of vertices on one side of a square cloth

enable Chebyshev:
Chebyshev is an algorithm delivered by Huaming Wang. Here is the PDF. This option is only for comparison.

enable pre-factorization on the finest level:
Enable it for direct solve on the finest level. Disable it for saving a ton of time in pre-computing.

save matrix in each level (including the finest level) in a LDU memory layout:
LDU memory layout saves the lower part, the diagonal and the upper part of a matrix seperately.
For performance issue, symmetric Gauss-Seidel iteration is only supported on this memory layout.

list of multigrid operations:
To customize a multigrid procedure, we offer 3 kinds of operations: DownSample, UpSample and Smoothing.

• DownSample: This operation sets up the coarsened problem based on current level and switches to the next coarsened level. Use it as "DS".
• UpSample: This operation updates information in the fined problem based on current level and switches to the next fined level. Use it as "US".
• Smoothing: This operation performs smoothing iterations on the current level. So far we have implemented:
  • Jacobi iteration: could be used if matrix is not stored in dense, use "Jacobi [N]" for [N] iterations.
  • Gauss-Seidel iteration: could be used if matrix is not store in dense and stored in LDU memory layout, use "GS [N]" for [N] iterations.
  • Direct solve: could be used if matrix is in the coarsest level and stored in dense, or in the finest level with [enable pre-factorization on the finest level] on, use it as "Direct".

list of objects in the scene:
This option is for simulation with collision. Define the COLLISION flag in code use enable it. So far we support these objects:

• Sphere: use "Sphere [cx] [cy] [cz] [r]" as a sphere centered in position (cx, cy, cz) with radius r.
• Plane: use "Plane [nx] [ny] [nz] [b]" as a plane whose analytical form is (nx, ny, nz)*(x, y, z)=b.
• Cylinder: use "Cylinder [cx] [cy] [r]" as a Cylinder which is infinitely long along z axis, centered in position (cx, cy, 0) and with radius r.

boundary conditions:
We have a hard coded "fixed vectices" boundary conditions.

For tet simulations:

Overview

[mesh file name]

[output directory of benckmark records]

[enable benchmark]

[scaling] [pre rotation] [post rotation]

[number of iterations in one frame] [enable Hessian] [enable Chebyshev] [enable pre-factorization on the finest level]

[relaxation parameter of Gauss-Seidel iteration]

[number of coarsened level]

[number of vertices in each coarsened level, begin from the coarsest level]

[save matrix in each level (including the finest level) in a dense matrix memory layout]

[save matrix in each level (including the finest level) in a LDU memory layout]

[number of multigrid operations]

[list of multigrid operations]

[parameter for Chebyshev]

[number of objects in the scene]

[list of objects in the scene]

Detail Explaination

Almost the same as the previous one, except:

mesh file name:
we provide some sample meshes in our project. You can generate mesh files in the same format to simulate your own meshes.

scaling, pre rotation, post rotation:
This is for getting rid of re-compilation while benchmarking. You can also hard code it for customization.

We are still working...

This code has not been re-written yet for people to read it easily. Contact [e-mail] if you have any problem.