AI & ML
A fourth-order dimensionally split exponential time differencing scheme with real and distinct pole rational approximation for non-linear reaction-diffusion systems
arXiv cs.NA0 views
arXiv:2611.14485v1 Announce Type: new Abstract: This paper presents a novel fourth-order, L-stable exponential time differencing (ETD) Runge-Kutta type scheme incorporating a dimensional splitting integrating factor method for the numerical solution of nonlinear reaction-diffusion systems. The method, ETDRK4RDP-IF, is obtained by approximating the matrix exponential operators in the classical dimensionally split ETDRK-IF scheme with an accurate fourth-order, L-acceptable rational function with real and distinct poles. The L-acceptability of the rational approximation guarantees effective damping of spurious oscillations arising from nonsmooth initial and/or boundary data and further eliminates complex arithmetic in the solution of the associated linear systems, thereby enhancing computational efficiency and making the scheme well-suited for parallel implementation in low-level programming languages such as Fortran and C++. Numerical experiments confirm the fourth-order accuracy for a range of reaction-diffusion problems with Dirichlet and Neumann boundary conditions, and demonstrate that it outperforms existing standard ETD methods in serial and parallel implementations, yielding CPU time reductions of up to a factor of 20.
Source：https://arxiv.org/abs/2611.14485PreviousShape Perturbation of the Galerkin Boundary Element Dirichlet-to-Neumann Matrix on Moving PolygonsNextNeural Networks with Local Converging Inputs for Solving the 3D Stokes Equations on Unstructured Meshes: Novel Techniques and Advances
Related posts
Hitting 200 Strokes: What the Signature Maker Does at Its Stroke Limit
0dev.to
A Lightweight, Open-Source Network Digital Twin Blueprint for IoT-Edge Environments
0arXiv cs.NI
Bridge: Optimizing Collective Communication Schedules in Reconfigurable Networks with Reusable Subrings
0arXiv cs.NI
SplitCom: Communication-efficient Split Federated Fine-tuning of LLMs via Temporal Compression
0arXiv cs.NI
Programmable GPU-Accelerated dApps for Real-Time Edge Inference and ISAC on NVIDIA Aerial Testbed
0arXiv cs.NI
PSL-RGHA: Parallel Split Learning with Reference Gradient Half-Space Alignment for Mitigating Gradient Divergence
0arXiv cs.NI