Related papers: Boundary-Conforming Finite Element Methods for Twi…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
Surface tension and contact angle measurements are fundamental characterization techniques relevant to thermal and fluidic applications. Drop shape analysis techniques for the measurement of interfacial tension are powerful, versatile and…
This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open…
We present an efficient approach of Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). The image registration framework…
An $hp$-adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law…
A general method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time, and 3D hypersurface meshes embedded in four-dimensional (4D) space time. In particular, we begin by dividing…
In this article we consider a priori error and pointwise estimates for finite element approximations of solutions to semilinear elliptic boundary value problems in d>=2 space dimensions, with nonlinearities satisfying critical growth…
Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…
Parametric finite element discretizations of constrained geometric flows must simultaneously address high-order geometric stiffness, mesh degeneration, and nonlinear global constraints. This paper develops a stabilized dual-SAV (scalar…
We consider a numerical scheme for the approximation of a system that couples the evolution of a two--dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been…
In the class of immersed boundary (IB) methods, the choice of the delta function plays a crucial role in transferring information between fluid and solid domains. Most prior work has used isotropic kernels that do not preserve the…
In this paper, our aim is to present (1) an embedded fracture model (EFM) for coupled flow and mechanics problem based on the dual continuum approach on the fine grid and (2) an upscaled model for the resulting fine grid equations. The…
This paper presents a general framework for calculating the dimension of spline spaces over arbitrary rectilinear partitions using the smoothing cofactor method. The approach extends existing dimension theory for polynomial splines over…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…
Off-the-shelf fused filament fabrication 3D printers are widely accessible and convenient, yet they exhibit quality loss at high speeds due to dynamic mis-synchronization between printhead motion and material extrusion systems, notably…
This study presents a spiral-based complete coverage strategy for ball-end milling on freeform surfaces, utilizing conformal slit mapping to generate milling trajectories that are more compact, smoother, and evenly distributed when…
A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the…