Related papers: An efficient GPU-based h-adaptation framework via …
High-order DG methods have become a popular technique in computational fluid dynamics because their accuracy increases spectrally in smooth solutions with the order of the approximation. However, their main drawback is that increasing the…
Graphics Processing Unit (GPU) computing is becoming an alternate computing platform for numerical simulations. However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of…
Similarity search, the task of identifying objects most similar to a given query object under a specific metric, has gathered significant attention due to its practical applications. However, the absence of coordinate information to…
We present the methodology of a photon-conserving, spatially-adaptive, ray-tracing radiative transfer algorithm, designed to run on multiple parallel Graphic Processing Units (GPUs). Each GPU has thousands computing cores, making them…
Fluid simulations are often performed using the incompressible Navier-Stokes equations (INSE), leading to sparse linear systems which are difficult to solve efficiently in parallel. Recently, kinetic methods based on the…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…
In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…
Ptychography is an emerging imaging technique that is able to provide wavelength-limited spatial resolution from specimen with extended lateral dimensions. As a scanning microscopy method, a typical two-dimensional image requires a number…
In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR software that works independently of the used element type,…
We introduce TransformerFusion, a transformer-based 3D scene reconstruction approach. From an input monocular RGB video, the video frames are processed by a transformer network that fuses the observations into a volumetric feature grid…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
The workload of real-time rendering is steeply increasing as the demand for high resolution, high refresh rates, and high realism rises, overwhelming most graphics cards. To mitigate this problem, one of the most popular solutions is to…
The Convex Hull algorithm is one of the most important algorithms in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is…
This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…
We propose a parallel graph-based data clustering algorithm using CUDA GPU, based on exact clustering of the minimum spanning tree in terms of a minimum isoperimetric criteria. We also provide a comparative performance analysis of our…
We present $k^{O(k^2)} m$ time algorithms for various problems about decomposing a given undirected graph by edge cuts or vertex separators of size $<k$ into parts that are ``well-connected'' with respect to cuts or separators of size $<k$;…
This paper proposes a novel heterogeneous grid convolution that builds a graph-based image representation by exploiting heterogeneity in the image content, enabling adaptive, efficient, and controllable computations in a convolutional…
Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…