Numerical Analysis
In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets…
Considering high speed following on expressway or highway, an improved car-following model is developed in this paper by introducing variable safety headway distance. Stability analysis of the new model is carried out using the control…
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical…
In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between…
Developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering. A desirable feature to have in a numerical formulation for multiscale…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied…
A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard…
CANDECOMP/PARAFAC (CPD) approximates multiway data by sum of rank-1 tensors. Our recent study has presented a method to rank-1 tensor deflation, i.e. sequential extraction of the rank-1 components. In this paper, we extend the method to…
In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, $L_{q}$ regularization with $q\in(0,1)$) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency.…
We present a way of constructing multi-time-step monolithic coupling methods for elastodynamics. The governing equations for constrained multiple subdomains are written in dual Schur form and enforce the continuity of velocities at system…
In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature…
In this paper the isogeometric Nystr\"om method is presented. It's outstanding features are: it allows the analysis of domains described by many different geometrical mapping methods in computer aided geometric design and it requires only…
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent…
The Fast Marching Method is a very popular algorithm to compute times-of-arrival maps (distances map measured in time units). Since their proposal in 1995, it has been applied to many different applications such as robotics, medical…
We present a novel computational framework for diffusive-reactive systems that satisfies the non-negative constraint and maximum principles on general computational grids. The governing equations for the concentration of reactants and…
Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the Navier-Stokes equations…
We propose a novel method for speeding up stochastic optimization algorithms via sketching methods, which recently became a powerful tool for accelerating algorithms for numerical linear algebra. We revisit the method of conditioning for…
We numerically analyze the possibility of turning off post-smoothing (relaxation) in geometric multigrid when used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsening…
Digital filter construction method, which is optimal by parametric sensitivity, based on using of non-canonical hypercomplex number systems is proposed and investigated. It is shown that the use of non-canonical hypercomplex number system…