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GPU-Accelerated Computing with Python 3 and CUDA
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This chapter explores how to solve the heat equation, a fundamental partial differential equation (PDE) used in science and engineering, such as weather forecasting. We will apply previously introduced concepts, including parallel execution of CUDA kernels and utilization of memory layouts, to optimize the heat equation solver. Solving the heat equation as a stencil problem is well-suited for GPUs because each grid point is updated using only its nearest neighbors, meaning the same computation is applied independently, which can be mapped onto the thousands of threads available on a GPU. Additionally, stencil computations involve structured access to memory, which aligns well with GPU memory hierarchies such as caches and shared memory, enabling high throughput and efficient latency hiding. Numba-CUDA will be utilized to accelerate the computations, providing practical experience in solving time-dependent PDEs on the GPU. Note that while an understanding...