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The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work…

A set of control points can determine a Bezier surface and a triangulated surface simultaneously. We prove that the triangulated surface becomes homeomorphic and ambient isotopic to the Bezier surface via subdivision. We also show that the…

State-of-the-art methods for quantifying wear in cylinder liners of large internal combustion engines require disassembly and cutting of the liner. This is followed by laboratory-based high-resolution microscopic surface depth measurement…

Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…

Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…

In computer-aided design (CAD), the ability to "reverse engineer" the modeling steps used to create 3D shapes is a long-sought-after goal. This process can be decomposed into two sub-problems: converting an input mesh or point cloud into a…

The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…

We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…

This paper addresses the problem of document image dewarping, which aims at eliminating the geometric distortion in document images for document digitization. Instead of designing a better neural network to approximate the optical flow…

The complex interaction between turbulence and the free surface in boundary layer shear flow created by a vertical surface-piercing wall is considered. A laboratory-scale device was built that utilizes a surface-piercing stainless steel…

Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…

This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the…

In this paper, we propose improved wall-treatment strategies for meshfree methods applied to turbulent flows. The goal is to enhance wall-function handling in simulations of high-Reynolds-number turbulent flows and to understand the…

Neural implicit surface reconstruction using volume rendering techniques has recently achieved significant advancements in creating high-fidelity surfaces from multiple 2D images. However, current methods primarily target scenes with…

It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In~this paper we will investigate in more detail the case of canal surfaces that are often…

This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In…

Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of…

A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approximations. The model is meant to probe the consequences of the…

Computational fluid dynamics (CFD) studies have been increasingly used for blood flow simulations in intracranial aneurysms (ICAs). However, despite the continuous progress of body-fitted CFD solvers, generating a high quality mesh is still…

Neural implicit shape representation has drawn significant attention in recent years due to its smoothness, differentiability, and topological flexibility. However, directly modeling the shape of a neural implicit surface, especially as the…