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We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
High-fidelity 3D Gaussian Splatting methods excel at capturing fine textures but often overlook model compactness, resulting in massive splat counts, bloated memory, long training, and complex post-processing. We present Micro-Splatting:…
We present a three-dimensional (3D) common-refinement method for non-matching meshes between discrete non-overlapping subdomains of incompressible fluid and nonlinear hyperelastic structure. To begin, we first investigate the accuracy of…
This paper presents a simple, efficient, and high-order accurate sliding-mesh interface approach to the spectral difference (SD) method. We demonstrate the approach by solving the two-dimensional compressible Navier-Stokes equations on…
An efficient hardware implementation for Simultaneous Localization and Mapping (SLAM) methods is of necessity for mobile autonomous robots with limited computational resources. In this paper, we propose a resource-efficient FPGA…
Feedback motion planning over cell decompositions provides a robust method for generating collision-free robot motion with formal guarantees. However, existing algorithms often produce paths with unnecessary bending, leading to slower…
Designing a freeform surface to reflect or refract light to achieve a target distribution is a challenging inverse problem. In this paper, we propose an end-to-end optimization strategy for an optical surface mesh. Our formulation leverages…
This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
SLAM technology plays a crucial role in indoor mapping and localization. A common challenge in indoor environments is the "double-sided mapping issue", where closely positioned walls, doors, and other surfaces are mistakenly identified as a…
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 a method to vibration analysis in order to on-line monitoring of milling process quality. Adapting envelope analysis to characterize the milling tool materials is an important contribution to the qualitative and…
This work explores a spatial printing method to fabricate continuous fiber-reinforced thermoplastic composites (CFRTPCs), which can achieve exceptional mechanical performance. For models giving complex 3D stress distribution under loads,…
Simultaneous Localization and Mapping (SLAM) technology enables the construction of environmental maps and localization, serving as a key technique for indoor autonomous navigation of mobile robots. Traditional SLAM methods typically…
We describe new methods for the construction of spiral toolpaths for high-speed machining. In the simplest case, our method takes a polygon as input and a number $\delta>0$ and returns a spiral starting at a central point in the polygon,…
Mapping a triangulated surface to 2D space (or a tetrahedral mesh to 3D space) is the most fundamental problem in geometry processing.In computational physics, untangling plays an important role in mesh generation: it takes a mesh as an…
We develop an operator splitting approach to solve diffeomorphic matching problems for sequences of surfaces in three-dimensional space. The goal is to smoothly match, at a very fast rate, finite sequences of observed 3D-snapshots extracted…
While feature association to a global map has significant benefits, to keep the computations from growing exponentially, most lidar-based odometry and mapping methods opt to associate features with local maps at one voxel scale. Taking…