Related papers: B-spline-Based ALE-MFS Framework for Evolving Doma…
We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation…
Optimal-order convergence in the $H^1$ norm is proved for an arbitrary Lagrangian-Eulerian interface tracking finite element method for the sharp interface model of two-phase Navier-Stokes flow without surface tension, using high-order…
In this paper we address anisotropic and inhomogeneous mean curvature flows with forcing and mobility, and show that the minimizing movements scheme converges to level set/viscosity solutions and to distributional solutions \textit{\`a la}…
This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…
In nature, limbless locomotion is adopted by a wide range of organisms at various length scales. Interestingly, undulatory, crawling and inching/looping gait constitutes a fundamental class of limbless locomotion and is often observed in…
Spectral methods are renowned for their high accuracy and efficiency in solving partial differential equations. The Fourier pseudo-spectral method is limited to periodic domains and suffers from Gibbs oscillations in non-periodic problems.…
In this paper, we introduce a direct method of moving spheres for the nonlocal fractional Laplacian $(-\triangle)^{\alpha/2}$ for $0<\alpha<2$, in which a key ingredient is the narrow region maximum principle. As immediate applications, we…
A Streamline Upwind Petrov-Galerkin (SUPG) finite element method for transient convection-diffusion-reaction equation in time-dependent domains is proposed. In particular, a convection dominated transient scalar problem is considered. The…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control…
We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on unstructured triangular meshes that is high order accurate in space and time and that also allows for time-accurate local time stepping…
Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…
Abstract: we present a framework for robust autonomous driving motion planning system in urban environments which includes trajectory refinement, trajectory interpolation, avoidance of static and dynamic obstacles, and trajectory tracking.…
A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be…
We present Advancing Front Mapping (AFM), a provably robust algorithm for the computation of surface mappings to simple base domains. Given an input mesh and a convex or star-shaped target domain, AFM installs a (possibly refined) version…
Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate…
We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving moving boundaries. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary…
Recent advancements in image animation have utilized diffusion models to breathe life into static images. However, existing controllable frameworks typically rely on Lagrangian motion guidance, where optical flow is estimated relative to…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
This study presents a meshfree two-dimensional fractional-order Element-Free Galerkin (2D f-EFG) method as a viable alternative to conventional mesh-based FEM for a numerical solution of (spatial) fractional-order differential equations…