160. Concurrency of the exponential integrators for the glioblastoma brain tumor simulations

Abstract:

This work delivers a rigorous concurrency assessment of three‑dimensional glioblastoma‑growth simulations that combine finite‑difference spatial discretisation with exponential‑integrator time stepping. Using the trace‑theory formalism, we decompose the solver into a directed acyclic graph of indivisible tasks, from which we derive closed‑form expressions for the critical path length, intrinsic parallelism and theoretical speed‑up. These analytic insights guide the construction of a production‑grade MATLAB / CUDA implementation that adheres to established high‑performance‑computing design principles.

Benchmarking on an NVIDIA RTX 2080 SUPER (3072 CUDA cores, 8 GB GDDR6) shows that the optimised code advances a 128^3 MRI‑derived test case by one nonlinear time step in 140 ms, achieving a 23x wall‑time reduction relative to an aggressively tuned multicore‑CPU baseline. The proposed framework therefore offers a transferable blueprint for engineering and analysing sparse‑PDE solvers across computational biomedicine, with direct utility for margin planning, radiotherapy scheduling and metastasis‑risk prognosis.

About the author:

Maciej Wozniak is an associated professor on Institute of Computer Science in AGH  University of Science and Technology, Kraków, Poland. He received his  master degree in Computer Science in 2013. He received his bachelor  degree in Business Management in 2015. In 2017 he received his Ph.D. in  computational science from AGH-UST. Since 2012 he is a member of Prof.  Maciej Paszynski research group, working primarily on fast parallel direct solvers for isogeometric finite element methods targeting  different parallel architectures.

Maciej Wozniak orcid.org