相关论文: Kinetic Solvers with Adaptive Mesh in Phase Space

This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…

Adaptive mesh refinement (AMR) offers a practical solution to reduce the computational cost and memory requirement of numerical simulations that use computational meshes. In this work, we introduce a novel smart methodology for adaptive…

3D representations of highly deformable 3D models, such as dynamic 3D meshes, have recently become very popular due to their wide applicability in various domains. This trend inevitably leads to a demand for storage and transmission of…

The impressive progress of the kinetic schemes in the solution of gas dynamics problems and the development of effective parallel algorithms for modern high performance parallel computing systems led to the development of advanced methods…

We introduce the atomic valence active space (AVAS), a simple and well-defined automated technique for constructing active orbital spaces for use in multi-configuration and multireference (MR) electronic structure calculations. Concretely,…

A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Boltzmann model equation is solved by the discrete velocity method with an…

Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…

When dealing with the steady-state multiscale radiative transfer equation (RTE) with heterogeneous coefficients, spatially localized low-rank structures are present in the angular space. This paper introduces an adaptive tailored finite…

In moving mesh methods, the underlying mesh is dynamically adapted without changing the connectivity of the mesh. We specifically consider the generation of meshes which are adapted to a scalar monitor function through equidistribution.…

A novel mesh refinement sensor is proposed for lattice Boltzmann methods (LBMs) applicable to either static or dynamic mesh refinement algorithms. The sensor exploits the kinetic nature of LBMs by evaluating the departure of distribution…

Modeling dynamics in the form of partial differential equations (PDEs) is an effectual way to understand real-world physics processes. For complex physics systems, analytical solutions are not available and numerical solutions are…

Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost…

When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…

Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the…

The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to…

For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or to by far too small time scales. To overcome this problem multiscale techniques are being…

The recently proposed discrete unified gas kinetic scheme (DUGKS) is a finite volume method for deterministic solution of the Boltzmann model equation with asymptotic preserving property. In DUGKS, the numerical flux of the distribution…

This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…

An active-sensing-based learning algorithm is proposed to solve the near-field beam alignment problem with the aid of wavenumber-domain transform matrices (WTMs). Specifically, WTMs can transform the antenna-domain channel into a sparse…

Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can be used to track discontinuities in the…