相关论文: Windowed space-time least-squares Petrov-Galerkin …
Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov barrier that affects transport-dominated problems. In this work, we build on the reduced dynamics given by Neural Galerkin schemes and propose to…
While deep learning has achieved remarkable success in solving partial differential equations (PDEs), it still faces significant challenges, particularly when the PDE solutions have low regularity or singularities. To address these issues,…
This research paper investigates the Adjoint Petrov-Galerkin (APG) method for reduced order models (ROM) and fluid dynamics governed by the incompressible Navier-Stokes equations. The Adjoint Petrov-Galerkin ROM, derived using the…
We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements,…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
Three kinds of Fragile Points Methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up of the previous study on the original FPM based…
We propose in this paper a Proper Generalized Decomposition (PGD) approach for the solution of problems in linear elastodynamics. The novelty of the work lies in the development of weak formulations of the PGD problems based on the…
Super-time-stepping (STS) methods provide an attractive approach for enabling explicit time integration of parabolic operators, particularly in large-scale, higher-dimensional kinetic simulations where fully implicit schemes are…
In this paper, we investigate a spectral Petrov-Galerkin method for fractional initial value problems. Singularities of the solution at the origin inherited from the weakly singular kernel of the fractional derivative are considered, and…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $\Omega\subset\mathbb{R}^2$, possibly occupied by piecewise homogeneous media with different propagation speeds.…
3D occupancy prediction is critical for comprehensive scene understanding in vision-centric autonomous driving. Recent advances have explored utilizing 3D semantic Gaussians to model occupancy while reducing computational overhead, but they…
We present a well-posed ultra-weak space-time variational formulation for the time-dependent version of the linear Schr\"odinger equation with an instationary Hamiltonian. We prove optimal inf-sup stability and introduce a space-time…
Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…
Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of values rather than being just a fixed integer/fraction as it…
A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the…
A least-squares formulation of the Moving Discontinuous Galerkin Finite Element Method with Interface Condition Enforcement (LS-MDG-ICE) is presented. This method combines MDG-ICE, which uses a weak formulation that separately enforces a…
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics,…
We propose a least-squares penalization as a means to extend the discontinuous Petrov-Galerkin (DPG) method with optimal test functions to a class of semilinear elliptic problems. The nonlinear contributions are replaced with independent…
As an improvement of the Meshless Local Petrov-Galerkin (MLPG), the Direct Meshless Local Petrov-Galerkin (DMLPG) method is applied here to the numerical solution of transient heat conduction problem. The new technique is based on direct…