相关论文: Even Order Explicit Symplectic Geometric Algorithm…

We consider path planning for a rigid spatial robot with 6 degrees of freedom (6 DOFs), moving amidst polyhedral obstacles. A correct, complete and practical path planner for such a robot has never been achieved, although this is widely…

In this paper, we explore scaling symmetries within the framework of symplectic geometry. We focus on the action $\Phi$ of the multiplicative group $G = \mathbb{R}^+$ on exact symplectic manifolds $(M, \omega,\theta)$, with $\omega =…

In this paper, we introduce a numerical solution of a stochastic partial differential equation (SPDE) of elliptic type using polynomial chaos along side with polynomial approximation at Sinc points. These Sinc points are defined by a…

Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems. In a QCQP, we are asked to minimize a (possibly nonconvex) quadratic function subject to a number of (possibly nonconvex) quadratic…

We review the general problem of finding a global rotation that transforms a given set of points and/or coordinate frames (the "test" data) into the best possible alignment with a corresponding set (the "reference" data). For 3D point data,…

There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…

We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of…

Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stiff problems. We study this issue in Physics-Informed Extreme…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Systematic enumeration and identification of unique 3D spatial topologies of complex engineering systems (such as automotive cooling systems, electric power trains, satellites, and aero-engines) are essential to navigation of these…

When time-dependent partial differential equations (PDEs) are solved numerically in a domain with curved boundary or on a curved surface, mesh error and geometric approximation error caused by the inaccurate location of vertices and other…

We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual…

Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized,…

The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…

Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

Efficient and accurate numerical simulation of seismic wave propagation is important in various Geophysical applications such as seismic full waveform inversion (FWI) problem. However, due to the large size of the physical domain and…

Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…

We apply the Gradient-Newton-Galerkin-Algorithm (GNGA) of Neuberger & Swift to find solutions to a semilinear elliptic Dirichlet problem on the region whose boundary is the Koch snowflake. In a recent paper, we described an accurate and…

High-order moving-mesh methods can effectively reduce numerical diffusion, but their formal accuracy typically relies on the regularity of the mesh velocity. This dependency creates a fundamental conflict in the numerical solution of…