Implicit and semi-implicit numerical schemes for the gradient flow of the formation of biological transport networks

DOI10.5802/smai-jcm.59zbMath1437.65095OpenAlexW2985384337MaRDI QIDQ2178652

Di Fang, Perthame, Benoît, Shih Jin, Peter Alexander Markowich

Publication date: 11 May 2020

Published in: SMAI Journal of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/smai-jcm.59

zbMATH Keywords

gradient flownumerical schemesbiological transport networks

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Classical flows, reactions, etc. in chemistry (92E20) Flows in porous media; filtration; seepage (76S05) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Nonlinear elliptic equations (35J60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Physiological flows (76Z05) Physiological flow (92C35) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items

Optimisation of Biological Transport Networks, Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation, A modified and efficient phase field model for the biological transport network, Discontinuous Galerkin methods for network patterning phase-field models, Energy-production-rate preserving numerical approximations to network generating partial differential equations, Supplementary variable method for structure-preserving approximations to partial differential equations with deduced equations

Cites Work

• Unnamed Item
• Unnamed Item
• Notes on a PDE system for biological network formation
• Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation
• A mesoscopic model of biological transportation networks
• ODE- and PDE-based modeling of biological transportation networks
• Analysis and applications of the exponential time differencing schemes and their contour integration modifications
• Biological transportation networks: Modeling and simulation
• Mathematical Analysis of a PDE System for Biological Network Formation