[petsc-dev] Using PETSC with GPUs
Barry Smith
bsmith at petsc.dev
Thu Jan 20 15:42:07 CST 2022
Some operations on the GPU are asynchronous, the CPU passes the kernel launch to the GPU and then immediately returns ready to do something else before the kernel is completed (or even started). Some like VecDot() where the result is stored in a CPU memory have to block until the kernel is complete and the result copied up to the CPU.
-log_view forces a the calls to PetscLogGpuTimeEnd() which has (for CUDA)
cerr = cudaEventRecord(petsc_gputimer_end,PetscDefaultCudaStream);CHKERRCUDA(cerr);
cerr = cudaEventSynchronize(petsc_gputimer_end);CHKERRCUDA(cerr);
cerr = cudaEventElapsedTime(>ime,petsc_gputimer_begin,petsc_gputimer_end);CHKERRCUDA(cerr);
petsc_gtime += (PetscLogDouble)gtime/1000.0; /* convert milliseconds to seconds */
which essentially causes the CPU to wait until the kernel is complete, hence your time with -log_view captures the full time to run the kernel.
So timing with GPUs can be a tricky business (when do you want to block and when do you not?) For your loop, you may want to use
PetscLogGpuTimeBegin()
> start = now()
>
> for (int i = 0; i < 10; i++) {
> MatMult(A, x, y);
> }
PetscLogGpuTimeEnd()
> end = now()
> print(end - start / 10)
> ```
Now after the loop it will wait until all the multiplies are completely done; giving a better view of the time it takes. If you did
> start = now()
>
> for (int i = 0; i < 10; i++) {
PetscLogGpuTimeBegin()
> MatMult(A, x, y);
PetscLogGpuTimeEnd()
> }
> end = now()
> print(end - start / 10)
> ```
You would wait a longer time because the CPU could not tell the GPU about the second kernel launch until the first kernel is completely done. Hence there would be no overlap of GPU computation and CPU kernel launches (which take a long time).
IMHO timing individual operations like a single MatMult() on GPUs only has a certain level of usefulness since you slow down the computation (by removing the asynchronous nature between the GPU and CPU) in order to get accurate times. It is better to time something like a complete line solver, nonlinear solve etc and not log at a finer granularity.
Barry
> On Jan 20, 2022, at 4:07 PM, Rohan Yadav <rohany at alumni.cmu.edu> wrote:
>
> Another small question -- I'm a little confused around timing GPU codes with PETSc. I have a code that looks like:
> ```
> start = now()
> for (int i = 0; i < 10; i++) {
> MatMult(A, x, y);
> }
> end = now()
> print(end - start / 10)
> ```
>
> If I run this program with `-vec_type cuda -mat_type aijcusparse`, the GPUs are indeed utilized, but the recorded time is very tiny (i imagine just tracking the cost of launching cuda kernels). However, if I add `-log_view` to the command line arguments, then the resulting time printed matches what is recorded by `nvprof`. What is the correct way to benchmark PETSc with GPUs without having -log_view turned on?
>
> Thanks,
>
> Rohan
>
> On Sat, Jan 15, 2022 at 7:37 AM Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>> wrote:
>
> Oh yes, you are correct for this operation since the handling of different nonzero pattern is not trivial to implement well for the GPU.
>
>> On Jan 15, 2022, at 1:17 AM, Rohan Yadav <rohany at alumni.cmu.edu <mailto:rohany at alumni.cmu.edu>> wrote:
>>
>> Scanning the source code for mpiseqaijcusparse confirms my thoughts -- when used with DIFFERENT_NONZERO_PATTERN, it falls back to calling MatAXPY_SeqAIJ, copying the data back over to the host.
>>
>> Rohan
>>
>> On Fri, Jan 14, 2022 at 10:16 PM Rohan Yadav <rohany at alumni.cmu.edu <mailto:rohany at alumni.cmu.edu>> wrote:
>>
>>
>> ---------- Forwarded message ---------
>> From: Rohan Yadav <rohany at alumni.cmu.edu <mailto:rohany at alumni.cmu.edu>>
>> Date: Fri, Jan 14, 2022 at 10:03 PM
>> Subject: Re: [petsc-dev] Using PETSC with GPUs
>> To: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
>>
>>
>> Ok, I'll try looking with greps like and see what I find.
>>
>> > My guess why your code is not using the seqaijcusparse is that you are not setting the type before you call MatLoad() hence it loads with SeqAIJ. -mat_type does not magically change a type once a matrix has a set type. I agree our documentation on how to make objects be GPU objects is horrible now.
>>
>> I printed out my matrices with the PetscViewer objects and can confirm that the type is seqaijcusparse. Perhaps for the way I'm using it (DIFFERENT_NONZERO_PATTERN) the kernel is unsupported? I'm not sure how to get any more diagnostic info about why the cuda kernel isn't called...
>>
>> Rohan
>>
>> On Fri, Jan 14, 2022 at 9:46 PM Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>> wrote:
>>
>> This changes rapidly and depends on if the backend is CUDA, HIP, Sycl, or Kokkos. The only way to find out definitively is with, for example,
>>
>> git grep MatMult_ | egrep -i "(cusparse|cublas|cuda)"
>>
>>
>> Because of our, unfortunately, earlier naming choices you need to kind of know what to grep for, for CUDA it may be cuSparse or cuBLAS
>>
>> Not yet merged branches may also have some operations that are still being developed.
>>
>> My guess why your code is not using the seqaijcusparse is that you are not setting the type before you call MatLoad() hence it loads with SeqAIJ. -mat_type does not magically change a type once a matrix has a set type. I agree our documentation on how to make objects be GPU objects is horrible now.
>>
>> Barry
>>
>>
>>> On Jan 15, 2022, at 12:31 AM, Rohan Yadav <rohany at alumni.cmu.edu <mailto:rohany at alumni.cmu.edu>> wrote:
>>>
>>> I was wondering if there is a definitive list for what operations are and aren't supported for distributed GPU execution. For some operations, like `MatMult`, it is clear that MPIAIJCUSPARSE implements MatMult from the documentation, but other operations it is unclear, such as MatMatMult. Another scenario is the MatAXPY kernel, which supposedly has a SeqAIJCUSPARSE implementation, which I take means that it can only execute on a single GPU. However, even if I pass -mat_type seqaijcusparse to the kernel it doesn't seem to utilize the GPU.
>>>
>>> Rohan
>>>
>>> On Fri, Jan 14, 2022 at 4:05 PM Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>> wrote:
>>>
>>> Just use 1 MPI rank.
>>>
>>> ------------------------------------------------------------------------------------------------------------------------
>>> Event Count Time (sec) Flop --- Global --- --- Stage ---- Total GPU - CpuToGpu - - GpuToCpu - GPU
>>> Max Ratio Max Ratio Max Ratio Mess AvgLen Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s Mflop/s Count Size Count Size %F
>>> ---------------------------------------------------------------------------------------------------------------------------------------------------------------
>>>
>>> --- Event Stage 0: Main Stage
>>>
>>> BuildTwoSided 1 1.0 1.8650e-013467.8 0.00e+00 0.0 2.0e+00 4.0e+00 1.0e+00 0 0 3 0 2 0 0 3 0 4 0 0 0 0.00e+00 0 0.00e+00 0
>>> MatMult 30 1.0 6.6642e+01 1.0 1.16e+10 1.0 6.4e+01 6.4e+08 1.0e+00 65100 91 93 2 65100 91 93 4 346 0 0 0.00e+00 31 2.65e+04 0
>>>
>>> From this it is clear the matrix never ended up on the GPU, but the vector did. For each multiply, it is copying the vector from the GPU to the CPU and then doing the MatMult on the CPU. If the MatMult was done on the GPU the file number in the row would be 100% indicating all the flops were done on the GPU and the fifth from the end value of 0 would be some large number, being the flop rate on the GPU.
>>>
>>>
>>>
>>>> On Jan 14, 2022, at 4:59 PM, Rohan Yadav <rohany at alumni.cmu.edu <mailto:rohany at alumni.cmu.edu>> wrote:
>>>>
>>>> A log_view is attached at the end of the mail.
>>>>
>>>> I am running on a large problem size (639 million nonzeros).
>>>>
>>>> > * I assume you are assembling the matrix on the CPU. The copy of data to the GPU takes time and you really should be creating the matrix on the GPU
>>>>
>>>> How do I do this? I'm loading the matrix in from a file, but I'm running the computation several times (and with a warmup), so I would expect that the data is copied onto the GPU the first time. My (cpu) code to do this is here: https://github.com/rohany/taco/blob/5c0a4f4419ba392838590ce24e0043f632409e7b/petsc/benchmark.cpp#L68 <https://github.com/rohany/taco/blob/5c0a4f4419ba392838590ce24e0043f632409e7b/petsc/benchmark.cpp#L68>.
>>>>
>>>> Log view:
>>>>
>>>> ---------------------------------------------- PETSc Performance Summary: ----------------------------------------------
>>>>
>>>> ./bin/benchmark on a named lassen75 with 2 processors, by yadav2 Fri Jan 14 13:54:09 2022
>>>> Using Petsc Release Version 3.16.3, unknown
>>>>
>>>> Max Max/Min Avg Total
>>>> Time (sec): 1.026e+02 1.000 1.026e+02
>>>> Objects: 1.200e+01 1.000 1.200e+01
>>>> Flop: 1.156e+10 1.009 1.151e+10 2.303e+10
>>>> Flop/sec: 1.127e+08 1.009 1.122e+08 2.245e+08
>>>> MPI Messages: 3.500e+01 1.000 3.500e+01 7.000e+01
>>>> MPI Message Lengths: 2.210e+10 1.000 6.313e+08 4.419e+10
>>>> MPI Reductions: 4.100e+01 1.000
>>>>
>>>> Flop counting convention: 1 flop = 1 real number operation of type (multiply/divide/add/subtract)
>>>> e.g., VecAXPY() for real vectors of length N --> 2N flop
>>>> and VecAXPY() for complex vectors of length N --> 8N flop
>>>>
>>>> Summary of Stages: ----- Time ------ ----- Flop ------ --- Messages --- -- Message Lengths -- -- Reductions --
>>>> Avg %Total Avg %Total Count %Total Avg %Total Count %Total
>>>> 0: Main Stage: 1.0257e+02 100.0% 2.3025e+10 100.0% 7.000e+01 100.0% 6.313e+08 100.0% 2.300e+01 56.1%
>>>>
>>>> ------------------------------------------------------------------------------------------------------------------------
>>>> See the 'Profiling' chapter of the users' manual for details on interpreting output.
>>>> Phase summary info:
>>>> Count: number of times phase was executed
>>>> Time and Flop: Max - maximum over all processors
>>>> Ratio - ratio of maximum to minimum over all processors
>>>> Mess: number of messages sent
>>>> AvgLen: average message length (bytes)
>>>> Reduct: number of global reductions
>>>> Global: entire computation
>>>> Stage: stages of a computation. Set stages with PetscLogStagePush() and PetscLogStagePop().
>>>> %T - percent time in this phase %F - percent flop in this phase
>>>> %M - percent messages in this phase %L - percent message lengths in this phase
>>>> %R - percent reductions in this phase
>>>> Total Mflop/s: 10e-6 * (sum of flop over all processors)/(max time over all processors)
>>>> GPU Mflop/s: 10e-6 * (sum of flop on GPU over all processors)/(max GPU time over all processors)
>>>> CpuToGpu Count: total number of CPU to GPU copies per processor
>>>> CpuToGpu Size (Mbytes): 10e-6 * (total size of CPU to GPU copies per processor)
>>>> GpuToCpu Count: total number of GPU to CPU copies per processor
>>>> GpuToCpu Size (Mbytes): 10e-6 * (total size of GPU to CPU copies per processor)
>>>> GPU %F: percent flops on GPU in this event
>>>> ------------------------------------------------------------------------------------------------------------------------
>>>> Event Count Time (sec) Flop --- Global --- --- Stage ---- Total GPU - CpuToGpu - - GpuToCpu - GPU
>>>> Max Ratio Max Ratio Max Ratio Mess AvgLen Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s Mflop/s Count Size Count Size %F
>>>> ---------------------------------------------------------------------------------------------------------------------------------------------------------------
>>>>
>>>> --- Event Stage 0: Main Stage
>>>>
>>>> BuildTwoSided 1 1.0 1.8650e-013467.8 0.00e+00 0.0 2.0e+00 4.0e+00 1.0e+00 0 0 3 0 2 0 0 3 0 4 0 0 0 0.00e+00 0 0.00e+00 0
>>>> MatMult 30 1.0 6.6642e+01 1.0 1.16e+10 1.0 6.4e+01 6.4e+08 1.0e+00 65100 91 93 2 65100 91 93 4 346 0 0 0.00e+00 31 2.65e+04 0
>>>> MatAssemblyBegin 1 1.0 3.1100e-07 1.1 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00e+00 0 0.00e+00 0
>>>> MatAssemblyEnd 1 1.0 1.9798e+01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 4.0e+00 19 0 0 0 10 19 0 0 0 17 0 0 0 0.00e+00 0 0.00e+00 0
>>>> MatLoad 1 1.0 3.5519e+01 1.0 0.00e+00 0.0 6.0e+00 5.4e+08 1.6e+01 35 0 9 7 39 35 0 9 7 70 0 0 0 0.00e+00 0 0.00e+00 0
>>>> VecSet 5 1.0 5.8959e-02 1.1 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00e+00 0 0.00e+00 0
>>>> VecScatterBegin 30 1.0 5.4085e+00 1.0 0.00e+00 0.0 6.4e+01 6.4e+08 1.0e+00 5 0 91 93 2 5 0 91 93 4 0 0 0 0.00e+00 0 0.00e+00 0
>>>> VecScatterEnd 30 1.0 9.2544e+00 2.5 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 6 0 0 0 0 6 0 0 0 0 0 0 0 0.00e+00 0 0.00e+00 0
>>>> VecCUDACopyFrom 31 1.0 4.0174e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00e+00 31 2.65e+04 0
>>>> SFSetGraph 1 1.0 4.4912e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00e+00 0 0.00e+00 0
>>>> SFSetUp 1 1.0 5.2595e+00 1.0 0.00e+00 0.0 4.0e+00 1.7e+08 1.0e+00 5 0 6 2 2 5 0 6 2 4 0 0 0 0.00e+00 0 0.00e+00 0
>>>> SFPack 30 1.0 3.4021e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00e+00 0 0.00e+00 0
>>>> SFUnpack 30 1.0 1.9222e-05 1.5 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00e+00 0 0.00e+00 0
>>>> ---------------------------------------------------------------------------------------------------------------------------------------------------------------
>>>>
>>>> Memory usage is given in bytes:
>>>>
>>>> Object Type Creations Destructions Memory Descendants' Mem.
>>>> Reports information only for process 0.
>>>>
>>>> --- Event Stage 0: Main Stage
>>>>
>>>> Matrix 3 0 0 0.
>>>> Viewer 2 0 0 0.
>>>> Vector 4 1 1792 0.
>>>> Index Set 2 2 335250404 0.
>>>> Star Forest Graph 1 0 0 0.
>>>> ========================================================================================================================
>>>> Average time to get PetscTime(): 3.77e-08
>>>> Average time for MPI_Barrier(): 8.754e-07
>>>> Average time for zero size MPI_Send(): 2.6755e-06
>>>> #PETSc Option Table entries:
>>>> -log_view
>>>> -mat_type aijcusparse
>>>> -matrix /p/gpfs1/yadav2/tensors//petsc/kmer_V1r.petsc
>>>> -n 20
>>>> -vec_type cuda
>>>> -warmup 10
>>>> #End of PETSc Option Table entries
>>>> Compiled without FORTRAN kernels
>>>> Compiled with full precision matrices (default)
>>>> sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8 sizeof(PetscScalar) 8 sizeof(PetscInt) 4
>>>> Configure options: --download-c2html=0 --download-hwloc=0 --download-sowing=0 --prefix=./petsc-install/ --with-64-bit-indices=0 --with-blaslapack-lib="/usr/tcetmp/packages/lapack/lapack-3.9.0-gcc-7.3.1/lib/liblapack.so /usr/tcetmp/packages/lapack/lapack-3.9.0-gcc-7.3.1/lib/libblas.so" --with-cc=/usr/tce/packages/spectrum-mpi/spectrum-mpi-rolling-release-gcc-8.3.1/bin/mpigcc --with-clanguage=C --with-cxx-dialect=C++17 --with-cxx=/usr/tce/packages/spectrum-mpi/spectrum-mpi-rolling-release-gcc-8.3.1/bin/mpig++ --with-cuda=1 --with-debugging=0 --with-fc=/usr/tce/packages/spectrum-mpi/spectrum-mpi-rolling-release-gcc-8.3.1/bin/mpigfortran --with-fftw=0 --with-hdf5-dir=/usr/tcetmp/packages/petsc/build/3.13.0/spack/opt/spack/linux-rhel7-power9le/xl_r-16.1/hdf5-1.10.6-e7e7urb5k7va3ib7j4uro56grvzmcmd4 --with-hdf5=1 --with-mumps=0 --with-precision=double --with-scalapack=0 --with-scalar-type=real --with-shared-libraries=1 --with-ssl=0 --with-suitesparse=0 --with-trilinos=0 --with-valgrind=0 --with-x=0 --with-zlib-include=/usr/include --with-zlib-lib=/usr/lib64/libz.so --with-zlib=1 CFLAGS="-g -DNoChange" COPTFLAGS="-O3" CXXFLAGS="-O3" CXXOPTFLAGS="-O3" FFLAGS=-g CUDAFLAGS=-std=c++17 FOPTFLAGS= PETSC_ARCH=arch-linux-c-opt
>>>> -----------------------------------------
>>>> Libraries compiled on 2022-01-14 20:56:04 on lassen99
>>>> Machine characteristics: Linux-4.14.0-115.21.2.1chaos.ch6a.ppc64le-ppc64le-with-redhat-7.6-Maipo
>>>> Using PETSc directory: /g/g15/yadav2/taco/petsc/petsc/petsc-install
>>>> Using PETSc arch:
>>>> -----------------------------------------
>>>>
>>>> Using C compiler: /usr/tce/packages/spectrum-mpi/spectrum-mpi-rolling-release-gcc-8.3.1/bin/mpigcc -g -DNoChange -fPIC "-O3"
>>>> Using Fortran compiler: /usr/tce/packages/spectrum-mpi/spectrum-mpi-rolling-release-gcc-8.3.1/bin/mpigfortran -g -fPIC
>>>> -----------------------------------------
>>>>
>>>> Using include paths: -I/g/g15/yadav2/taco/petsc/petsc/petsc-install/include -I/usr/tcetmp/packages/petsc/build/3.13.0/spack/opt/spack/linux-rhel7-power9le/xl_r-16.1/hdf5-1.10.6-e7e7urb5k7va3ib7j4uro56grvzmcmd4/include -I/usr/include -I/usr/tce/packages/cuda/cuda-11.1.0/include
>>>> -----------------------------------------
>>>>
>>>> Using C linker: /usr/tce/packages/spectrum-mpi/spectrum-mpi-rolling-release-gcc-8.3.1/bin/mpigcc
>>>> Using Fortran linker: /usr/tce/packages/spectrum-mpi/spectrum-mpi-rolling-release-gcc-8.3.1/bin/mpigfortran
>>>> Using libraries: -Wl,-rpath,/g/g15/yadav2/taco/petsc/petsc/petsc-install/lib -L/g/g15/yadav2/taco/petsc/petsc/petsc-install/lib -lpetsc -Wl,-rpath,/usr/tcetmp/packages/lapack/lapack-3.9.0-gcc-7.3.1/lib -L/usr/tcetmp/packages/lapack/lapack-3.9.0-gcc-7.3.1/lib -Wl,-rpath,/usr/tcetmp/packages/petsc/build/3.13.0/spack/opt/spack/linux-rhel7-power9le/xl_r-16.1/hdf5-1.10.6-e7e7urb5k7va3ib7j4uro56grvzmcmd4/lib -L/usr/tcetmp/packages/petsc/build/3.13.0/spack/opt/spack/linux-rhel7-power9le/xl_r-16.1/hdf5-1.10.6-e7e7urb5k7va3ib7j4uro56grvzmcmd4/lib -Wl,-rpath,/usr/tce/packages/cuda/cuda-11.1.0/lib64 -L/usr/tce/packages/cuda/cuda-11.1.0/lib64 -Wl,-rpath,/usr/tce/packages/spectrum-mpi/ibm/spectrum-mpi-rolling-release/lib -L/usr/tce/packages/spectrum-mpi/ibm/spectrum-mpi-rolling-release/lib -Wl,-rpath,/usr/tce/packages/gcc/gcc-8.3.1/rh/usr/lib/gcc/ppc64le-redhat-linux/8 -L/usr/tce/packages/gcc/gcc-8.3.1/rh/usr/lib/gcc/ppc64le-redhat-linux/8 -Wl,-rpath,/usr/tce/packages/gcc/gcc-8.3.1/rh/usr/lib/gcc -L/usr/tce/packages/gcc/gcc-8.3.1/rh/usr/lib/gcc -Wl,-rpath,/usr/tce/packages/gcc/gcc-8.3.1/rh/usr/lib64 -L/usr/tce/packages/gcc/gcc-8.3.1/rh/usr/lib64 -Wl,-rpath,/usr/tce/packages/gcc/gcc-8.3.1/rh/usr/lib -L/usr/tce/packages/gcc/gcc-8.3.1/rh/usr/lib -llapack -lblas -lhdf5_hl -lhdf5 -lm /usr/lib64/libz.so -lcuda -lcudart -lcufft -lcublas -lcusparse -lcusolver -lcurand -lstdc++ -ldl -lmpiprofilesupport -lmpi_ibm_usempi -lmpi_ibm_mpifh -lmpi_ibm -lgfortran -lm -lgfortran -lm -lgcc_s -lquadmath -lpthread -lquadmath -lstdc++ -ldl
>>>> -----------------------------------------
>>>>
>>>> On Fri, Jan 14, 2022 at 1:43 PM Mark Adams <mfadams at lbl.gov <mailto:mfadams at lbl.gov>> wrote:
>>>> There are a few things:
>>>> * GPU have higher latencies and so you basically need a large enough problem to get GPU speedup
>>>> * I assume you are assembling the matrix on the CPU. The copy of data to the GPU takes time and you really should be creating the matrix on the GPU
>>>> * I agree with Barry, Roughly 1M / GPU is around where you start seeing a win but this depends on a lot of things.
>>>> * There are startup costs, like the CPU-GPU copy. It is best to run one mat-vec, or whatever, push a new stage and then run the benchmark. The timing for this new stage will be separate in the log view data. Look at that.
>>>> - You can fake this by running your benchmark many times to amortize any setup costs.
>>>>
>>>> On Fri, Jan 14, 2022 at 4:27 PM Rohan Yadav <rohany at alumni.cmu.edu <mailto:rohany at alumni.cmu.edu>> wrote:
>>>> Hi,
>>>>
>>>> I'm looking to use PETSc with GPUs to do some linear algebra operations, like SpMV, SPMM etc. Building PETSc with `--with-cuda=1` and running with `-mat_type aijcusparse -vec_type cuda` gives me a large slowdown from the same code running on the CPU. This is not entirely unexpected, as things like data transfer costs across the PCIE might erroneously be included in my timing. Are there some examples of benchmarking GPU computations with PETSc, or just the proper way to write code in PETSc that will work for CPUs and GPUs?
>>>>
>>>> Rohan
>>>
>>
>
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