Advances in Numerical Methods for Complex Systems

The field of numerical methods for complex systems is rapidly evolving, with a focus on developing innovative and efficient algorithms for solving partial differential equations, simulating complex phenomena, and analyzing large datasets. Recent research has led to significant advancements in areas such as finite element methods, multigrid techniques, and stochastic simulations. Notably, the development of new numerical schemes, such as the multigrid method for CutFEM and the kernel compression method for distributed-order fractional partial differential equations, has improved the accuracy and efficiency of simulations. Additionally, the application of machine learning techniques and high-performance computing has enabled the solution of complex problems in fields such as materials science, fluid dynamics, and biology. Some noteworthy papers in this area include the work on a finite element framework for simulating residential burglary, which demonstrates the potential of numerical methods for modeling complex social phenomena, and the development of a cubed sphere fast multipole method, which enables efficient simulations of particle interactions on the sphere. Overall, the field is moving towards the development of more sophisticated and specialized numerical methods, with a focus on addressing specific challenges and applications.

Sources

A finite element framework for simulating residential burglary in realistic urban geometries

A multigrid method for CutFEM and its implementation on GPU

Complementary bodies in sphere packing

Substepping the Material Point Method

Comparison of three random field sampling methods for high-resolution Bayesian inversion with application to a plane stress problem

Surface Stokes Without Inf-Sup Condition

Sparse, Geometry- and Material-Aware Bases for Multilevel Elastodynamic Simulation

A stability-enhanced nonstandard finite difference framework for solving one and two-dimensional nonlocal differential equations

A Cubed Sphere Fast Multipole Method

A kernel compression method for distributed-order fractional partial differential equations

A convergent Fourier spectral Galerkin method for the fractional Camassa-Holm equation

Analysis-Aware Defeaturing of Dirichlet Features

Lagrangian Simulation Volume-Based Contour Tree Simplification

Exact $\ell^\infty$-separation radius of Sobol' sequences in dimension 2

Reduced basis solvers for unfitted methods on parameterized domains

Implementation of Milstein Schemes for Stochastic Delay-Differential Equations with Arbitrary Fixed Delays

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