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The GPU accelerated PixelCounting method is most useful for models with large number of exterior solar shading surfaces (see slide 12 here). There is a difference in performance with a good dedicated GPU, however, an integrated GPU still does much better than the CPU-based method for large number of solar shading surfaces (seen in the previously referenced slide, 12 min vs 50 min for dedicated vs integrated respectively). There is a threshold (about 128-1024 shading surfaces depending on GPU) where the traditional CPU-based method is still slightly faster than the GPU accelerated PixelCounting approach.

Are you sure the lack of a dedicated GPU is slowing down the E+ simulations by 50% or more? A dedicated GPU will improve simulation time over an integrated GPU only if you have a large number (1000+) of exterior solar shading surfaces OR a large number (100s) of interior surfaces within a zone. Otherwise, it is likely there is some other issue slowing down your simulations unrelated to PixelCounting and the GPU.

If it is the lack of a dedicated GPU slowing down your simulations then I would find the most recent gaming or workstation GPU available to you in your price range. I have not done a large parametric study to see how different GPUs affect simulation time and what is the most sensitive parameter on the GPU (number of CUDA cores, memory bandwidth, PCIe connection, GB of memory, etc.). But most dedicated gaming or workstation GPUs will be better than an integrated GPU.