A review of level-set methods and some recent applications
We review some of the recent advances in level-set methods and their applications. In
particular, we discuss how to impose boundary conditions at irregular domains and free …
particular, we discuss how to impose boundary conditions at irregular domains and free …
INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems
S Wu, B Lu - Journal of Computational Physics, 2022 - Elsevier
Abstract Machine learning has been successfully applied to various fields in computational
science and engineering. In this paper, we propose interfaced neural networks (INNs) to …
science and engineering. In this paper, we propose interfaced neural networks (INNs) to …
Sharp interface approaches and deep learning techniques for multiphase flows
We present a review on numerical methods for simulating multiphase and free surface flows.
We focus in particular on numerical methods that seek to preserve the discontinuous nature …
We focus in particular on numerical methods that seek to preserve the discontinuous nature …
An extension to Voro++ for multithreaded computation of Voronoi cells
Voro++ is a software library written in C++ for computing the Voronoi tessellation, a
technique in computational geometry that is widely used for analyzing systems of particles …
technique in computational geometry that is widely used for analyzing systems of particles …
Power diagrams and sparse paged grids for high resolution adaptive liquids
We present an efficient and scalable octree-inspired fluid simulation framework with the
flexibility to leverage adaptivity in any part of the computational domain, even when …
flexibility to leverage adaptivity in any part of the computational domain, even when …
A mesh-free method using piecewise deep neural network for elliptic interface problems
In this paper, we propose a novel mesh-free numerical method for solving the elliptic
interface problems based on deep learning. We approximate the solution by the neural …
interface problems based on deep learning. We approximate the solution by the neural …
Optimal local truncation error method for solution of 3-D Poisson equation with irregular interfaces and unfitted Cartesian meshes as well as for post-processing
Recently the optimal local truncation error method (OLTEM) has been developed for the 2-D
Poisson equation for heterogeneous materials with irregular interfaces and unfitted …
Poisson equation for heterogeneous materials with irregular interfaces and unfitted …
Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface
In this paper we propose a second-order accurate numerical method to solve elliptic
problems with discontinuous coefficients (with general non-homogeneous jumps in the …
problems with discontinuous coefficients (with general non-homogeneous jumps in the …
An efficient meshfree method based on Pascal polynomials and multiple-scale approach for numerical solution of 2-D and 3-D second order elliptic interface problems
Ö Oruç - Journal of Computational Physics, 2021 - Elsevier
In this work, we propose an efficient meshfree method based on Pascal polynomials and
multiple-scale approach for numerical solutions of two-dimensional (2-D) and three …
multiple-scale approach for numerical solutions of two-dimensional (2-D) and three …
On two-phase flow solvers in irregular domains with contact line
We present numerical methods that enable the direct numerical simulation of two-phase
flows in irregular domains. A method is presented to account for surface tension effects in a …
flows in irregular domains. A method is presented to account for surface tension effects in a …