相关论文: Phase-space iterative solvers

We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…

Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…

We introduce a new regularized interface method for proving existence of weak solutions to nonlinear moving boundary problems with low-regularity interfaces. We study a fluid-poroelastic structure interaction (FPSI) problem coupling the…

Power iteration has been generalized to solve many interesting problems in machine learning and statistics. Despite its striking success, theoretical understanding of when and how such an algorithm enjoys good convergence property is…

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

How can one fully harness the power of physics encoded in relativistic $N$-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a…

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

We present a new method for constructing equilibrium phase models for stellar systems, which we call the iterative method. It relies on constrained, or guided evolution, so that the equilibrium solution has a number of desired parameters…

We define a non-iterative transformation method for Blasius equation with moving wall or surface gasification. The defined method allows us to deal with classes of problems in boundary layer theory that, depending on a parameter, admit…

This work serves as a primer to our efforts in arriving at convergence estimates for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The fixed stress split iterative…

We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…

Detecting changepoints in a one-dimensional signal is a classical yet fundamental problem. The fused lasso provides an elegant convex formulation that produces a stepwise estimate of the mean, but quantifying the uncertainty of the detected…

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

Small-scale plasticity problems are often characterised by different patterning behaviours ranging from macroscopic down to the atomistic scale. In successful models of such complex behaviour, its origin lies within non-convexity of the…

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…

A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…

The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…

Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…

Aussel et al. (J Optim Theory Appl 170 818-837 2016) introduced the concept of projected solutions for the quasi-variational inequalities with a non-self constraint map, that is, the case where the constraint map may take values outside the…

Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…