A MATLAB-linked solver to find fuel depletion in a PWR, a suggested VVER-1000 type.
A matrix constructive method for the analytic-numerical solution of coupled partial differential systems
In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation , where is an arbitrary square complex matrix and ia s matrix such that the real part of the eigenvalues of the matrix is positive. Given an admissible error and a finite domain , and analytic-numerical solution whose error is uniformly upper bounded by in , is constructed.
A Method of Characteristics Solving the Initial-Boundary Value Problem of a Hyperbolic Differential Equation of Second Order.
A mixed formulation of a sharp interface model of stokes flow with moving contact lines
Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking...
A model of macroscale deformation and microvibration in skeletal muscle tissue
This paper deals with modeling the passive behavior of skeletal muscle tissue including certain microvibrations at the cell level. Our approach combines a continuum mechanics model with large deformation and incompressibility at the macroscale with chains of coupled nonlinear oscillators. The model verifies that an externally applied vibration at the appropriate frequency is able to synchronize microvibrations in skeletal muscle cells. From the numerical analysis point of view, one faces...
A modified Cayley transform for the discretized Navier-Stokes equations
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform of the...
A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems.
A mountain pass method for the numerical solution of semilinear wave equations.
A multidomain spectral collocation method for the Stokes problem.
A multigrid method for distributed parameter estimation problems.
A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction
A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.
A Multiscale Model Reduction Method for Partial Differential Equations
We propose a multiscale model reduction method for partial differential equations. The main purpose of this method is to derive an effective equation for multiscale problems without scale separation. An essential ingredient of our method is to decompose the harmonic coordinates into a smooth part and a highly oscillatory part so that the smooth part is invertible and the highly oscillatory part is small. Such a decomposition plays a key role in our construction of the effective equation. We show...
A “natural” norm for the method of characteristics using discontinuous finite elements : 2D and 3D case
A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case
We consider the numerical approximation of a first order stationary hyperbolic equation by the method of characteristics with pseudo time step k using discontinuous finite elements on a mesh . For this method, we exhibit a “natural” norm || ||h,k for which we show that the discrete variational problem is well posed and we obtain an error estimate. We show that when k goes to zero problem (resp. the || ||h,k norm) has as a limit problem (Ph) (resp. the || ||h norm) associated to the...
A new approach for simultaneous shape and topology optimization based on dynamic implicit surface function
A new approach for simultaneous shape and topology optimization based on dynamic implicit surface function
A new approach for the analysis of Vortex Methods in two and three dimensions
A new approach to solve a nonlinear wave equation.
A new conservative difference scheme for the general Rosenau-RLW equation.
A new conservative finite difference scheme for Boussinesq paradigm equation
A family of nonlinear conservative finite difference schemes for the multidimensional Boussinesq Paradigm Equation is considered. A second order of convergence and a preservation of the discrete energy for this approach are proved. Existence and boundedness of the discrete solution on an appropriate time interval are established. The schemes have been numerically tested on the models of the propagation of a soliton and the interaction of two solitons. The numerical experiments demonstrate that the...