-<span class=hljs-keyword >end</span></code></pre> <p>From the benchmark results, it is shown that the GPU did not perform better than the CPU in general (but there were some exceptions). Furthermore, the <code>Memory estimate</code> and <code>allocs estimate</code> statistics from the GPU are much larger than those from the CPU. This is probably due to the design that all the data transfer happens in the <code>rhs!</code> function and thus the memory cost is extremely high when transferring data repeatedly between the CPU and GPU. </p> <p>In addition, the results indicate that the GPU performs better with 2D and 3D examples than with 1D examples. That is because GPUs are designed to handle a large number of parallel tasks, and 2D and 3D problems usually offer more parallelism compared to 1D problems. Essentially, the more data you can process simultaneously, the more efficiently you can utilize the GPU. 1D problems may not be complex enough to take full advantage of the GPU parallel processing capability.</p> <h2 id=future_work ><a href="#future_work" class=header-anchor >Future Work</a></h2> <p>The future work is listed here, ranging from specific to more general, from top to bottom:</p> <ol> <li><p>Resolve <a href="https://github.com/huiyuxie/trixi_cuda/issues/9">Issue #9</a> and <a href="https://github.com/huiyuxie/trixi_cuda/issues/11">Issue #11</a> (and any upcoming issues) </p> <li><p>Complete the prototype for the remaining kernels (please refer to the Kernel to be Implemented from the <a href="https://github.com/czha/TrixiGPU.jl/blob/legacy/README.md">README.md</a> file).</p> <li><p>Update <a href="https://github.com/trixi-framework/Trixi.jl/pull/1604">PR #1604</a> and make it merged into the repository</p> <li><p>Optimize CUDA kernels to improve performance (especially data transfer, please refer to the kernel optimization part)</p> <li><p>Prototype the GPU kernels for other DG solvers (for example, <code>DGMulti</code>, etc.)</p> <li><p>Extend the single-GPU support to multi-GPU support (similarly, from single-thread to multi-thread)</p> <li><p>Broaden compatibility to other GPU types beyond Nvidia (such as those from Apple, Intel, and AMD)</p> </ol> <h2 id=acknowledgements ><a href="#acknowledgements" class=header-anchor >Acknowledgements</a></h2> <p>I would like to express my gratitude to Google, the Julia community, and my mentors (<a href="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/ranocha">Hendrik Ranocha</a>, <a href="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/sloede">Michael Schlottke-Lakemper</a>, and <a href="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/jlchan">Jesse Chan</a>) for this enriching experience during the Google Summer of Code 2023 program. This opportunity to participate, enhance my skills, and contribute to the advancement of Julia has been both challenging and rewarding.</p> <p>Special thanks go to my GSoC mentor <a href="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/ranocha">Hendrik Ranocha</a> (@ranocha) and another person from JuliaGPU <a href="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/maleadt"> Tim Besard</a> (@maleadt, though he is not my mentor), whose guidance and support throughout our regular discussions have been instrumental in answering my questions and overcoming hurdles. The Julia community is incredibly welcoming and supportive, and I am proud to have been a part of this endeavor.</p> <p>I am filled with appreciation for this fantastic summer of learning and development, and I look forward to seeing the continued growth of Julia and the contributions of its vibrant community.</p> <div class=page-foot > <div class=copyright > © <a href="https://github.com/trixi-framework/Trixi.jl/blob/main/AUTHORS.md" target=_blank rel="noopener noreferrer">The Trixi Authors</a>. Last modified: July 08, 2025. Website built with <a href="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/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>. </div> </div> </div>
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