相关论文: Fast variable density 3-D node generation
A so-called grid-overlay finite difference method (GoFD) was proposed recently for the numerical solution of homogeneous Dirichlet boundary value problems of the fractional Laplacian on arbitrary bounded domains. It was shown to have…
Spacetime discontinuous Galerkin (SDG) finite element methods are used to solve such PDEs involving space and time variables arising from wave propagation phenomena in important applications in science and engineering. To support an…
Transforming planar mesoscale devices into precise 3-D architectures is vital for next-generation flexible electronics, implants, and adaptive optics, yet wafer-based manufacturing to free-standing 3-D structures remain elusive. We…
Previous efforts have managed to generate production-ready 3D assets from text or images. However, these methods primarily employ NeRF or 3D Gaussian representations, which are not adept at producing smooth, high-quality geometries required…
Standard finite element methods employ an element-wise assembly strategy. The element's contribution to the system matrix is formed by a loop over quadrature points. This concept is also used in fictitious domain methods, which perform…
Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local…
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…
Mesh generation plays a crucial role in scientific computing. Traditional mesh generation methods, such as TFI and PDE-based methods, often struggle to achieve a balance between efficiency and mesh quality. To address this challenge,…
Generative reconstruction methods compute the 3D configuration (such as pose and/or geometry) of a shape by optimizing the overlap of the projected 3D shape model with images. Proper handling of occlusions is a big challenge, since the…
We present a new method for numerical hydrodynamics which uses a multidimensional generalisation of the Roe solver and operates on an unstructured triangular mesh. The main advantage over traditional methods based on Riemann solvers, which…
We present LT3SD, a novel latent diffusion model for large-scale 3D scene generation. Recent advances in diffusion models have shown impressive results in 3D object generation, but are limited in spatial extent and quality when extended to…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the…
In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…
We propose a novel method to up-sample volumetric functions with generative neural networks using several orthogonal passes. Our method decomposes generative problems on Cartesian field functions into multiple smaller sub-problems that can…
Generative models for 2D images has recently seen tremendous progress in quality, resolution and speed as a result of the efficiency of 2D convolutional architectures. However it is difficult to extend this progress into the 3D domain since…
There is a great need in several areas of astrophysics and space-physics to carry out high order of accuracy, divergence-free MHD simulations on spherical meshes. This requires us to pay careful attention to the interplay between mesh…
Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid…
A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion…
A numerical method is presented for first-principle simulations of charged colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile for colloid-solvent boundaries, efficient mesoscopic simulations are enabled for…