This work delivers a rigorous concurrency assessment of three\u2011dimensional glioblastoma\u2011growth simulations that combine finite\u2011difference spatial discretisation with exponential\u2011integrator time stepping. Using the trace\u2011theory formalism, we decompose the solver into a directed acyclic graph of indivisible tasks, from which we derive closed\u2011form expressions for the critical path length, intrinsic parallelism and theoretical speed\u2011up. These analytic insights guide the construction of a production\u2011grade MATLAB \/ CUDA implementation that adheres to established high\u2011performance\u2011computing design principles.<\/p>\n\n\n\n
Benchmarking on an NVIDIA RTX 2080 SUPER (3072 CUDA cores, 8 GB GDDR6) shows that the optimised code advances a 128^3 MRI\u2011derived test case by one nonlinear time step in 140 ms, achieving a 23x wall\u2011time reduction relative to an aggressively tuned multicore\u2011CPU baseline. The proposed framework therefore offers a transferable blueprint for engineering and analysing sparse\u2011PDE solvers across computational biomedicine, with direct utility for margin planning, radiotherapy scheduling and metastasis\u2011risk prognosis.<\/p>\n\n\n\n
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