In general, it is difficult to use the Newton–Krylov methods to solve the large-scale multivariable nonequilibrium reaction–diffusion systems. In this paper, by employing two new semi-implicit discretization schemes to construct the preconditioners, the preconditioned Newton–Krylov methods are presented to solve the multidimensional problems. These methods cannot only improve the number of iter...

In this paper we present some classes of high-order semi-Lagrangian schemes for solving the periodic one-dimensional Vlasov-Poisson system in phase-space on uniform grids. We prove that the distribution function f(t, x, v) and the electric field E(t, x) converge in the L2 norm with a rate of O ( ∆t + h + hm+1 ∆t ) , where m is the degree of the polynomial reconstruction, and ∆t and h are respec...

We present a semi-Lagrangian method for advection–diffusion and incompressible Navier–Stokes equations. The focus is on constructing stable schemes of secondorder temporal accuracy, as this is a crucial element for the successful application of semi-Lagrangian methods to turbulence simulations. We implement the method in the context of unstructured spectral/hp element discretization, which allo...

In this paper we present a novel semi-implicit time-discretization of the level set method introduced in [8] for fluid-structure interaction problems. The idea stems form a linear stability analysis derived on a simplified one-dimensional problem. The semi-implicit scheme relies on a simple filter operating as a post-processing on the level set function. It applies to multiphase flows driven by...

This article concernes the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search a solution in an infinite dimensional Banach space having only a finite number of data available. In this sense the situation is applicalble to a large variety of applications where a measurement process delivers a discretization of an i...

In this paper we construct a hierarchy of arbitrary high (even) order accurate explicit time propagators for semi-discrete second order hyperbolic systems. An accurate semi-discrete problem is obtained by approximating the corresponding spatial derivatives using high order accurate finite difference operators satisfying the summation by parts rule. In order to obtain a strictly stable semi-disc...

What kinds of data does Label Propagation (LP) work best on? Can we justify the solution of LP from a theoretical standpoint? LP is a semisupervised learning algorithm that is widely used to predict unobserved node labels on a network (e.g., user’s gender on an SNS). Despite its importance, its theoretical properties remain mostly unexplored. In this paper, we answer the above questions by inte...

In this paper, we study a family of semisupervised learning algorithms for “aligning” different data sets that are characterized by the same underlying manifold. The optimizations of these algorithms are based on graphs that provide a discretized approximation to the manifold. Partial alignments of the data sets—obtained from prior knowledge of their manifold structure or from pairwise correspo...

In this article, we consider a fully discrete stabilized finite element method based on two local Gauss integrations for the two-dimensional time-dependent Navier–Stokes equations. It focuses on the lowest equal-order velocity–pressure pairs. Unlike the other stabilized method, the present approach does not require specification of a stabilization parameter or calculation of higher-order deriva...

We present a novel approach to low-dimensional neighbor embedding for visualization, based on formulating an information retrieval based neighborhood preservation cost function as Maximum satisfiability on a discretized output display. The method has a rigorous interpretation as optimal visualization based on the cost function. Unlike previous lowdimensional neighbor embedding methods, our form...