The field of numerical methods for complex systems is rapidly evolving, with a focus on developing innovative and efficient algorithms for solving nonlinear problems. Researchers are exploring new approaches to improve the accuracy and stability of numerical solutions, such as the use of splitting methods, invariant-region-preserving schemes, and anisotropic goal-oriented error control. These advancements have significant implications for a wide range of applications, including fluid dynamics, biological transportation networks, and neuromorphic circuits. Noteworthy papers include the development of a variable metric splitting algorithm for neuromorphic circuits simulation and an anisotropic goal-oriented error estimator for convection-diffusion-reaction equations. The variable metric splitting algorithm has been shown to be scalable and amenable to the simulation of large-scale neuromorphic circuits, while the anisotropic goal-oriented error estimator has demonstrated efficiency and robustness in adaptive mesh refinement.
Advances in Numerical Methods for Complex Systems
Sources
Characterizing and computing solutions to regularized semi-discrete optimal transport via an ordinary differential equation
Quasi-optimal error estimate for the approximation of the elastic flow of inextensible curves
Accurate stochastic simulation of nonlinear reactions between closest particles
Unified interface flux evaluation in a general discontinuous Galerkin spectral element framework
Error analysis of a Euler finite element scheme for Natural convection model with variable density
Splitting Method for Stochastic Navier-Stokes Equations
Unconditionally optimal error Estimate of a linearized Second-order Fully Discrete Finite Element Method for the bioconvection flows with concentration dependent viscosity
Robust and scalable nonlinear solvers for finite element discretizations of biological transportation networks
Optimal Order Space-Time Discretization Methods for the Nonlinear Stochastic Elastic Wave Equations with Multiplicative Noise
An invariant-region-preserving scheme for a convection-reaction-Cahn-Hilliard multiphase model of biofilm growth in slow sand filters
Anisotropic space-time goal-oriented error control and mesh adaptivity for convection-diffusion-reaction equations
Coupling approaches with non-matching grids for classical linear elasticity and bond-based peridynamic models in 1D
Variable Metric Splitting Methods for Neuromorphic Circuits Simulation