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Conditioning diffusion and flow models have proven effective for super-resolving small-scale details in natural images.However, in physical sciences such as weather, super-resolving small-scale details poses significant challenges due to:…
The high-frequency Helmholtz equation on the entire space is truncated into a bounded domain using the perfectly matched layer (PML) technique and subsequently, discretized by the higher-order finite element method (FEM) and the continuous…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
Continuous normalizing flows (CNFs) can model data distributions with expressive infinite-length architectures. But this modeling involves computationally expensive process of solving an ordinary differential equation (ODE) during maximum…
The coupling effects in multiphysics processes are often neglected in designing multiscale methods. The coupling may be described by a non-positive definite operator, which in turn brings significant challenges in multiscale simulations. In…
In the mathematical problem of linear hydrodynamic stability for shear flows against Tollmien-Schlichting perturbations, the continuity equation for the perturbation of the velocity is replaced by a Poisson equation for the pressure…
This article presents an immersed finite element (IFE) method for solving the typical three-dimensional second order elliptic interface problem with an interface-independent Cartesian mesh. The local IFE space on each interface element…
In this paper, we develop a novel well-balanced Point-Average-Moment PolynomiAl-interpreted (PAMPA) numerical method for solving the two-dimensional shallow water equations with temperature gradients on unstructured triangular meshes. The…
Many combinatorial problems deal with preferences and violations, the goal of which is to find solutions with the minimum cost. Weighted constraint satisfaction is a framework for modeling such problems, which consists of a set of cost…
The aim of this paper is to investigate the unstable nature of pressure computation focusing on incompressible flow modeling through the projection-based particle methods. A new approach from the original viewpoint of the momentum…
Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…
Although FFT-based methods are renowned for their numerical efficiency and stability, traditional discretizations fail to capture material interfaces that are not aligned with the grid, resulting in suboptimal accuracy. To address this…
Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares…
Linear elastic fracture mechanics admit analytic solutions that have low regularity at crack tips. Current numerical methods for partial differential equations (PDEs) of this type suffer from the constraint of such low regularity, and fail…
The present study aims to extend the applicability of the static-boundary absorption method in phase-resolving CFD simulations outside the conventional shallow-water waves limit. Even though this method was originally formulated for…
In this paper, a new method, named the Fragile Points Method (FPM), is developed for computer modeling in engineering and sciences. In the FPM, simple, local, polynomial, discontinuous and Point-based trial and test functions are proposed…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
This contribution presents a novel Windowed Green Function (WGF) method for the solution of problems of wave propagation, scattering and radiation for structures which include open (dielectric) waveguides, waveguide junctions, as well as…
Solving partial differential equations (PDEs) with discontinuous solutions , such as shock waves in multiphase viscous flow in porous media , is critical for a wide range of scientific and engineering applications, as they represent sudden…
This paper introduces a new algorithm to improve the accuracy of numerical phase-averaging in oscillatory, multiscale, differential equations. Phase-averaging is a timestepping method which averages a mapped variable to remove highly…