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The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…
Fluid flow is a widely applied physical problem, crucial in various fields. Due to the highly nonlinear and chaotic nature of fluids, analyzing fluid-related problems is exceptionally challenging. Computational fluid dynamics (CFD) is the…
To facilitate the understanding and to quantitatively assess the material transport in fluids, a modern characterisation method has emerged in fluid dynamics in the last decades footed in dynamical systems theory. It allows to examine the…
In this paper, we introduce a novel approach that combines multiresolution (MR) techniques with the flux reconstruction (FR) method to accurately and effciently simulate compressible flows. We achieve further enhancements in effciency…
High-speed stereo PIV-measurements have been performed in a turbulent boundary layer at Re$_{\theta}$ of 9800 in order to elucidate the coherent structures. Snapshot proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD)…
In this paper, we extend the unsplit staggered mesh scheme (USM) for 2D magnetohydrodynamics (MHD) (Lee and Deane, 2009) to a full 3D MHD scheme. The scheme is a finite-volume Godunov method consisting of a constrained transport (CT) method…
We consider constructing a surface from a given set of point cloud data. We explore two fast algorithms to minimize the weighted minimum surface energy in [Zhao, Osher, Merriman and Kang, Comp.Vision and Image Under., 80(3):295-319, 2000].…
The recent application of Fourier Based Iterative Reconstruction Method (FIRM) has made it possible to achieve high-quality 2D images from a fan beam Computed Tomography (CT) scan with a limited number of projections in a fast manner. The…
3D Gaussian Splatting (3DGS) has emerged as a promising 3D reconstruction technique. The traditional 3DGS training pipeline follows three sequential steps: Gaussian densification, Gaussian projection, and color splatting. Despite its…
Simulating turbulence is critical for many societally important applications in aerospace engineering, environmental science, the energy industry, and biomedicine. Large eddy simulation (LES) has been widely used as an alternative to direct…
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too…
Real-time 3D reconstruction of surgical scenes plays a vital role in computer-assisted surgery, holding a promise to enhance surgeons' visibility. Recent advancements in 3D Gaussian Splatting (3DGS) have shown great potential for real-time…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
We present an efficient, elastic 3D LiDAR reconstruction framework which can reconstruct up to maximum LiDAR ranges (60 m) at multiple frames per second, thus enabling robot exploration in large-scale environments. Our approach only…
Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) have advanced 3D reconstruction and novel view synthesis, but remain heavily dependent on accurate camera poses and dense viewpoint coverage. These requirements limit their…
We present a novel way of approaching image-based 3D reconstruction based on radiance fields. The problem of volumetric reconstruction is formulated as a non-linear least-squares problem and solved explicitly without the use of neural…
Quantum computing shows substantial potential in accelerating simulations and alleviating memory bottlenecks in computational fluid dynamics (CFD), owing to its inherent properties of superposition and entanglement. The lattice Boltzmann…
High-resolution remote sensing images (RSIs) are crucial for Earth observation applications, yet acquiring them is often limited by sensor constraints and costs. In recent years, generative super-resolution (SR) methods, particularly…
While 3D Gaussian Splatting (3DGS) excels in static scene modeling, its extension to dynamic scenes introduces significant challenges. Existing dynamic 3DGS methods suffer from either over-smoothing due to low-rank decomposition or feature…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…