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The accurate representation of fine-detailed cloth wrinkles poses significant challenges in computer graphics. The inherently non-uniform structure of cloth wrinkles mandates the employment of intricate discretization strategies, which are…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
In this paper, the Combined Finite-Discrete Element Method (FDEM) has been applied to analyze the deformation of anisotropic geomaterials. In the most general case geomaterials are both non-homogeneous and non-isotropic. With the aim of…
This paper presents an improved non-ordinary state-based peridynamics (NOSB PD) framework for modelling the elastoplastic behaviour and damage of geomaterials, such as soil, rock, and concrete, under quasi static conditions. Conventional…
We formulate and solve a Bayesian inverse Navier-Stokes (N-S) problem that assimilates velocimetry data in order to jointly reconstruct a 3D flow field and learn the unknown N-S parameters, including the boundary position. By hardwiring a…
Manifold learning techniques for nonlinear dimension reduction assume that high-dimensional feature vectors lie on a low-dimensional manifold, then attempt to exploit manifold structure to obtain useful low-dimensional Euclidean…
Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…
We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional maps framework, but rather than promoting isometries we focus instead on near-conformal maps that…
Steepest descent is central in variational mathematics. We present a new transparent existence proof for curves of near-maximal slope --- an influential notion of steepest descent in a nonsmooth setting. We moreover show that for…
A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…
Recently, neural implicit surfaces learning by volume rendering has become popular for multi-view reconstruction. However, one key challenge remains: existing approaches lack explicit multi-view geometry constraints, hence usually fail to…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…
We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
In this article we introduce an asymptotic preserving scheme designed to compute the solution of a two dimensional elliptic equation presenting large anisotropies. We focus on an anisotropy aligned with one direction, the dominant part of…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…