Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov–)Galerkin projection process that enforces dynamics evolve in low-dimensional subspace original state space. Frequently, resulting reduced-order model (ROM) violates intrinsic physical properties full-order (e.g., global conservation, Lagrangian structure, state-variable b...

This paper extends the dual-Petrov-Galerkin method proposed by Shen [16] and further developed by Yuan, Shen and Wu [23] to several integrable and non-integrable fifth-order KdV type equations. These fifth-order equations arise in modeling different wave phenomena and involve various nonlinear terms. The method is implemented to compute the solitary wave solutions of these equations and the num...

We use the global collocation method, the first and the third-order shear deformation plate theories, the Mori–Tanaka technique to homogenize material properties, and approximate the trial solution with multiquadric radial basis functions to analyze free vibrations of functionally graded plates. Frequencies computed by the present method are found to agree well with those from the analytical so...

A non-overlapping domain decomposition algorithm combining boundary element method with meshless local Petrov-Galerkin method is presented for solving the boundary value problem with discontinuous coefficient in this paper. The static relaxation parameter is employed to speed up the convergence rate. The convergence range and the optimal value of static relaxation parameter are studied, but the...

Computational simulation of steam flow and heat transfer in power plant condensers on the basis of the threedimensional mathematical model for the flow through porous media is presented. In order to solve the mathematical model of steam flow and heat transfer in power plant condensers, the Streamline Upwind Petrov-Galerkin finite element method is applied. By comparison of the results of simula...

Using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-D domains with complex geometry. The Petrov-Galerkin finite element formulation is adopted to avoid numerical oscillations. Turbulence is modeled using the two equation k-ω model. The discretized equations are written in the form o...

Using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-D domains with complex geometry. The Petrov-Galerkin finite element formulation is adopted to avoid numerical oscillations. Turbulence is modeled using the two equation k-ω model. The discretized equations are written in the form o...

We propose and analyze deterministic multilevel approximations for Bayesian inversion of operator equations with uncertain distributed parameters, subject to additive gaussian measurement data. The algorithms use a multilevel (ML) approach based on deterministic, higher order quasi-Monte Carlo (HoQMC) quadrature for approximating the high-dimensional expectations, which arise in the Bayesian es...