Related papers: Naturally curved quadrilateral mesh generation usi…

We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…

We describe here a method to generate high-definition arbitrary laser beam shapes and profiles useful to many applications, ranging from optical patterning and lithography to optical trapping of microscopic particles and ultracold atoms.…

We describe a method for constructing $n$-orthogonal coordinate systems in constant curvature spaces. The construction proposed is a modification of Krichever's method for producing orthogonal curvilinear coordinate systems in the…

Accuracy of a simulation is strongly depend on the grid quality. Here, quality means orthogonality at the boundaries and quasi-orthogonality within the critical regions, smoothness, bounded aspect ratios, solution adaptive behaviour, etc.…

We consider a discontinuous Galerkin method for the numerical solution of boundary value problems in two-dimensional domains with curved boundaries. A key challenge in this setting is the potential loss of convergence order due to…

With the recent advances in machine learning for quantum chemistry, it is now possible to predict the chemical properties of compounds and to generate novel molecules. Existing generative models mostly use a string- or graph-based…

Domain warping is a technique commonly used in creative coding to distort graphics and add visual interest to a work. The approach has the potential to be used in 3D art as mesh vertices can be efficiently warped using a vertex shader in a…

The finite element method, finite difference method, finite volume method and spectral method have achieved great success in solving partial differential equations. However, the high accuracy of traditional numerical methods is at the cost…

The generation of production-ready quad-dominant meshes is a cornerstone of modern 3D content creation. Generating anisotropic quad-dominant meshes from point clouds is challenging, as existing methods are typically limited to producing…

We propose a graph-based sweep algorithm for solving the steady state, mono-energetic discrete ordinates on meshes of high-order curved mesh elements. Our spatial discretization consists of arbitrarily high-order discontinuous Galerkin…

In order to obtain a metasurface structure capable of filtering the light of a specific wavelength in the visible band, traditional method usually traverses the space consisting of possible designs, searching for a potentially satisfying…

The creation of manufacturable and editable 3D shapes through Computer-Aided Design (CAD) remains a highly manual and time-consuming task, hampered by the complex topology of boundary representations of 3D solids and unintuitive design…

We present a new software package, "HybridOctree_Hex," for adaptive all-hexahedral mesh generation based on hybrid octree and quality improvement with Jacobian control. The proposed HybridOctree_Hex begins by detecting curvatures and narrow…

Molecular conformer generation is a fundamental task in computational chemistry. Several machine learning approaches have been developed, but none have outperformed state-of-the-art cheminformatics methods. We propose torsional diffusion, a…

This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…

In this paper, we extend the classical quadrilateral based hierarchical Poincar\'e-Steklov (HPS) framework to triangulated geometries. Traditionally, the HPS method takes as input an unstructured, high-order quadrilateral mesh and relies on…

A conforming discontinuous Galerkin finite element method is introduced for solving the biharmonic equation. This method, by its name, uses discontinuous approximations and keeps simple formulation of the conforming finite element method at…

We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes. In…

Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…

While recent generative models for 2D images achieve impressive visual results, they clearly lack the ability to perform 3D reasoning. This heavily restricts the degree of control over generated objects as well as the possible applications…