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In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the…

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric…

We present and study theoretically a new design approach for obtaining wide angle, highly efficient, all-dielectric metasurfaces. As a concrete example we focus on optimizing flat beam deflector for both the infra-red and visible spectral…

Despite the promising results of multi-view reconstruction, the recent neural rendering-based methods, such as implicit surface rendering (IDR) and volume rendering (NeuS), not only incur a heavy computational burden on training but also…

Resonant metasurfaces are of paramount importance in addressing the growing demand for reduced thickness and complexity, while ensuring high optical efficiency. This becomes particularly crucial in overcoming fabrication challenges…

In this paper we introduce three complementary three-dimensional weighted quadratic enrichment strategies to improve the accuracy of local histopolation on tetrahedral meshes. The first combines face and interior weighted moments…

Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we…

Generative models for 3D object synthesis have seen significant advancements with the incorporation of prior knowledge distilled from 2D diffusion models. Nevertheless, challenges persist in the form of multi-view geometric inconsistencies…

We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on octree-based 3D block-structured collocated grids with distributed computational architectures. Our approach…

We present a suite of techniques for jointly optimizing triangle meshes and shading models to match the appearance of reference scenes. This capability has a number of uses, including appearance-preserving simplification of extremely…

Topology change is a challenging problem for 4D reconstruction of dynamic scenes. In the classic volumetric fusion-based framework, a mesh is usually extracted from the TSDF volume as the canonical surface representation to help estimating…

We present MeshODE, a scalable and robust framework for pairwise CAD model deformation without prespecified correspondences. Given a pair of shapes, our framework provides a novel shape feature-preserving mapping function that continuously…

Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface.…

To satisfy the expected plethora of computation-heavy applications, federated edge learning (FEEL) is a new paradigm featuring distributed learning to carry the capacities of low-latency and privacy-preserving. To further improve the…

Creating high-fidelity 3D meshes with arbitrary topology, including open surfaces and complex interiors, remains a significant challenge. Existing implicit field methods often require costly and detail-degrading watertight conversion, while…

Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient…

This paper introduces a novel framework called DTNet for 3D mesh reconstruction and generation via Disentangled Topology. Beyond previous works, we learn a topology-aware neural template specific to each input then deform the template to…

Mesh generation is a crucial step in numerical simulations, significantly impacting simulation accuracy and efficiency. However, generating meshes remains time-consuming and requires expensive computational resources. In this paper, we…

Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functions, which assert to what extent a given object exhibits some…

This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…