Related papers: Collision-Based Hybrid Method for Two-Dimensional …
Partitioning transportation networks into balanced and spatially coherent traffic zones is a fundamental yet computationally challenging task in intelligent transportation systems. The resulting optimization problem exhibits dense…
The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed on a time-dependent surface. Only elementary tangential…
We present a globally convergent method for the solution of frictionless large deformation contact problems for hyperelastic materials. The discretisation uses the mortar method which is known to be more stable than node-to-segment…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
The second moment method is a linear acceleration technique which couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent…
A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a…
The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov $n$-widths of the…
In this paper we present a numerical approach to solve the Navier-Stokes equations on moving domains with second-order accuracy. The space discretization is based on the ghost-point method, which falls under the category of unfitted…
We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties…
Conventional gradient descent methods compute the gradients for multiple variables through the partial derivative. Treating the coupled variables independently while ignoring the interaction, however, leads to an insufficient optimization…
Solving large-scale nonlinear minimization problems is computationally demanding. Nonlinear multilevel minimization (NMM) methods explore the structure of the underlying minimization problem to solve such problems in a computationally…
We present a hybrid partitioned deep learning framework for the reduced-order modeling of fluid-structure interaction. Using the discretized Navier-Stokes in the arbitrary Lagrangian-Eulerian reference frame, we generate the full-order flow…
In this paper, we present an efficient fully spectral approximation scheme for exploring the one-dimensional steady-state neutron transport equation. Our methodology integrates the spectral-(Petrov-)Galerkin scheme in the spatial dimension…
This work is about a new two-level solver for Helmholtz equations discretized by finite elements. The method is inspired by two-grid methods for finite-difference Helmholtz problems as well as by previous work on two-level…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
We consider a nonlinear mixed-dimensional model for simulating gas transport in shale formation. The mathematical model consists of a coupled system of nonlinear equations, where flow within fractures is represented using a…
A convolutional neural network-based classifier is elaborated to retrace the initial orientation of deformed nucleus-nucleus collisions by integrating multiple typical experimental observables. The isospin-dependent…
The generalized Crank-Nicolson method is employed to obtain numerical solutions of the two-dimensional time-dependent Schrodinger equation. An adapted alternating-direction implicit method is used, along with a high-order finite difference…
We propose a neural network-based approach for collision detection with deformable objects. Unlike previous approaches based on bounding volume hierarchies, our neural approach does not require an update of the spatial data structure when…
The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…