Projective Jacobi and Gauss-Seidel on the GPU for Non-Smooth Multi-Body Systems

This source code includes the dense Jacobi (JORProx) and Gauss-Seidel (SORProx) GPU methods described in the paper

G. Nützi et al. , Projective Jacobi and Gauss-Seidel on the GPU for Non-Smooth Multi-Body Systems, 2014 , download : 1 or 2

The corresponding master thesis should be consulted only in the case of being interested in the details of certain GPU variants (see below).

This source code includes also the sparse JORProx Velocity GPU methods which is based on the following master thesis of Thierry Baasch available here 1

Installation & Dependencies

To build the performance tests (MatrixMultiply, Prox, etc.) you need the built tool cmake. The performance tests only depend on the matrix library Eigen at least version 3. Download it and install it on your system. You need CUDA installed on your system as well, download and install the latest CUDA API and Drivers.

Download the latest CudaFramework code:

    $ git clone https://github.com/gabyx/CudaFramework.git CudaFramework

Make a build directory and navigate to it:

    $ mkdir Build
    $ cd Build

Invoke cmake in the Build directory:

    $ cmake ../CudaFramework

The cmake script will find Eigen and Cuda if you installed it in a system wide folder (e.g /usr/local/)

Finally, build the performance tests:

    $ make all 
    $ make install

To build in parallel use the -jN flag in the make commmand, where Ndenotes the number of parallel threads to use.

Supported Platforms

The code has been tested on Linux and OS X with compilers clang and gcc. It should work for Windows as well, but has not been tested.

##Example Usage

The target PerformanceProx contains the parallel GPU implementation of the projective overrelaxed Jacobi (JORProx) and succesive overrelaxed Gauss-Seidel (SORProx, SORProxRelaxed) iterations used in multi-body dynamics. The target PerformanceMatrix contains the performance test of the efficient parallel matrix-multiplication kernel which is used for the JORProx implementation. The target GaussSeidelTest contains the test launches of the parallel linear Gauss-Seidel algorithm.

The performance tests are all written in the same structure. A performance tests of any kind of application can be specified with the PerformanceTest template class which accepts a test method as template argument. For the kernel performance tests mainly used in this project, the test method KernelTestMethod is of main interest. It is used for profiling/checking a certain GPU implementation (ProxTestVariant see below) against a serial CPU implementation. The results are saved in an XML file, with all output provided by the test method (e.g. KernelTestMethod). A python notebookpython/ParseXML.pynb is provided as an example to parse the performance tests output XML.

The following example shows how a performance test for the SORProx GPU Variant 1 is launched (target: PerformaceProx):

    typedef KernelTestMethod< /* Specify a kernel test method */ 
    
        KernelTestMethodSettings<false,true,0> ,  /* Specify the general kernel test method settings */ 
        
        ProxTestVariant< /* Specify the specific variant of the kernel test method */ 
            
            ProxSettings< /* All settings for the prox test variant */ 
        
               double,                  /* use double floating point precision */ 
               SeedGenerator::Fixed<5>, /* the seed for the random value generator for the test data */ 
               false,                   /* Write the test data to a file (matlab style) */ 
               1,                       /* Max. iterations of the prox iteration */
               false,                   /* Abort iteration if prox iteration converged */
               10,                      /* Convergence check every 10 iterations */
               true,                    /* Compare the GPU implementation to the exact serial replica on th CPU */
               ProxPerformanceTestSettings<3000,20,4000,3>,                /* Problem sizes from 3000 contacts to 4000 in steps of 20, generate 3 random test problems per problem size*/
               SorProxGPUVariantSettings<1,ConvexSets::RPlusAndDisk,true>  /* Use the GPU Variant 1, align the memory on the GPU for coalesced access!*/
            >
            
        >
        
    > test1;
    
    PerformanceTest<test1> A("SorProxVariant1D"); /* output file written to: SorProxVariant1D***.xml*/
    A.run();

Understanding JORProx and SORProx

To understand the workflow of the performance tests and application of the JORProx and SORProx, the user is encouraged to understand the basic workflow of the ProxTestVariant in ProxTestVariant.hpp. This class contains the basic initialization of the used matrices for the numerical iterations, the two important functions ProxTestVariant::runOnGPU() and ProxTestVariant::runOnCPU() which run the specified variant (e.g. SORProx GPU Variant 1 in the above example) on the CPU or the GPU, and a check routine ProxTestVariant::checkResults() which compares the results from the GPU to the CPU. The function call ProxTestVariant::runOnGPU() calls the runGPUProfile() function of the templated type ProxTestVariant::m_gpuVariant.

The GPU variants for the type m_gpuVariant of the JORProx and SORProx can be found in SorProxGPUVariant.hpp and JorProxGPUVariant.hpp. These files will help the most in understanding the source code together with the paper.

Each GPU variant class (e.g. JorProxGPUVariant, SorProxGPUVariant) contains certain variants (ennumerated with ids 1,2,3, ...) which mostly correspond to fixed GPU settings (block dimension, threads per block etc...). The descriptions of these variants are consistent with the master thesis (and hopefully also the paper). A GPU variant class (e.g. JorProxGPUVariant, SorProxGPUVariant) has a initializeTestProblem() function which fills the iteration matrices with random values (keeping the problem size fixed!). They also have runGPUProfile() and runGPUPlain() functions which run the specified variant id (e.g variant 1 of SorProxGPUVariant in the example above) with or without timing information.

To get at the bottom of the source code, that means to the actual code of the prox iteration, consider the kernels A and B of all variants in SorProxGPUVariant (see runKernel() function). This variant is described in the paper in detail. Kernels A and B are launched sequentially over the iteration matrix T_dev as shown in the following:

    for(m_nIterGPU=0; m_nIterGPU< m_nMaxIterations ; m_nIterGPU++){

            // Swap pointers of old and new on the device
            std::swap(x_old_dev.m_pDevice, x_new_dev.m_pDevice);

            for(int kernelAIdx = 0; kernelAIdx < loops; kernelAIdx++){

               //cudaThreadSynchronize();
               proxGPU::sorProxContactOrdered_1threads_StepA_kernelWrap<SorProxSettings1>(
                  mu_dev,x_new_dev,T_dev,d_dev,
                  t_dev,
                  kernelAIdx,
                  pConvergedFlag_dev,
                  m_absTOL,m_relTOL);

               proxGPU::sorProx_StepB_kernelWrap<SorProxSettings1>(
                  t_dev,
                  T_dev,
                  x_new_dev,
                  kernelAIdx
                  );

            }
    }

The core of the GPU kernel implementations can be found in the file ProxGPU.cu, KernelsProx.cuh and with the C++ wrapper calls in ProxGPU.hpp.

Interfacing with Own Code

The best way to use the SORProx or JORProx GPU implementations right out of the box is to instantiate the following variant types somewhere in your code:

   JorProxGPUVariant< JorProxGPUVariantSettingsWrapper<PREC,5,ConvexSets::RPlusAndDisk,true,1000,true,10,false, TemplateHelper::Default>, ConvexSets::RPlusAndDisk > m_jorGPUVariant;

   SorProxGPUVariant< SorProxGPUVariantSettingsWrapper<PREC,1,ConvexSets::RPlusAndDisk,true,1000,true,10,true,  TemplateHelper::Default >,  ConvexSets::RPlusAndDisk > m_sorGPUVariant;

Please see the file ProxSettings.hpp for the settings of SorProxGPUVariantSettingsWrapper and JorProxGPUVariantSettingsWrapper, the number 1000 denotes the maximal number of global prox iterations. These variants are the fastest methods so far (at least for the NIVIDIA GTX 580), you can try to tweak the settings in ProxKernelSettings.hpp for the JORProx and SORProx to gain better speeds for your GPU.

Launching the iterations would look similar to this example:

        m_jorGPUVariant.setSettings(m_settings.m_MaxIter,m_settings.m_AbsTol,m_settings.m_RelTol);
        gpuSuccess = m_jorGPUVariant.runGPUPlain(P_front,m_T,P_back,m_d,m_mu);
        m_globalIterationCounter = m_jorGPUVariant.m_nIterGPU;
        /* OR */
        m_sorGPUVariant.setSettings(m_settings.m_MaxIter,m_settings.m_AbsTol,m_settings.m_RelTol);
        gpuSuccess = m_sorGPUVariant.runGPUPlain(P_front,m_T,P_back,m_d,m_mu);
        m_globalIterationCounter = m_jorGPUVariant.m_nIterGPU;

Matrices m_T and m_d are built as described in the paper. Vector m_mu are the friction coefficients for all contacts which consist of a normal and two tangential forces. The percussions P_back and P_front are contact ordered and each contact tuple consits of (normal percussion, tangential percussion 1, tangential percussion 2, see the description in the paper).

Example Usage Sparse JORProx Velocity

In this section some short explanations of the sparse JORProx scheme which iterates in the velocities should be given. This implementation is based on the master thesis of Thierry Baasch available here 1 and is closely related to the implementation of

Million Body Simulations of Granular Dynamics on the GPU,” H. Mazhar, T. Heyn, A. Tasora, M. Anitescu, D. Negrut, accepted, SIAM Conference on Computational Science and Engineering, Reno, NV, 2011

We used a specialized segmented reduction kernel adapted from ModernGPU for the velocity update of the bodies.

Tutorial to come!

Licensing

This source code is released under GNU GPL 3.0.

Author and Acknowledgements

CudaFramework was written by Gabriel Nützi. Source code from ModernGPU has been used, see CudaModern folder in /include/CudaFramework

gabyx / CudaFramework