Search results for "Matrix"

Order optimal preconditioners for fully implicit Runge-Kutta schemes applied to the bidomain equations

2010

The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge–Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time-stepping operator in the proper Sobolev spaces, we show that the preconditioned systems have bounded condition numbers given that the Runge–Kutta scheme is A-stable and irreducible with an invertible coefficient matrix. A new proof of order optimality of the preconditioners for the one-leg discretization in time of the bidomain equations is also presented. The theoretical results are verified by numerical experiments. Additionally, the concept of weakly po…

Monotonic solution of heterogeneous anisotropic diffusion problems

2013

Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of…

Time-harmonic elasticity with controllability and higher-order discretization methods

2008

The time-harmonic solution of the linear elastic wave equation is needed for a variety of applications. The typical procedure for solving the time-harmonic elastic wave equation leads to difficulties solving large-scale indefinite linear systems. To avoid these difficulties, we consider the original time dependent equation with a method based on an exact controllability formulation. The main idea of this approach is to find initial conditions such that after one time-period, the solution and its time derivative coincide with the initial conditions.The wave equation is discretized in the space domain with spectral elements. The degrees of freedom associated with the basis functions are situa…

A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems

2010

In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…

State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve.

2004

We study the nitrogen binding curve with the density matrix renormalization group (DMRG) and single-reference and multireference coupled cluster (CC) theory. Our DMRG calculations use up to 4000 states and our single-reference CC calculations include up to full connected hextuple excitations. Using the DMRG, we compute an all-electron benchmark nitrogen binding curve, at the polarized, valence double-zeta level (28 basis functions), with an estimated accuracy of 0.03mE_h. We also assess the performance of more approximate DMRG and CC theories across the nitrogen curve. We provide an analysis of the relative strengths and merits of the DMRG and CC theory under different correlation condition…

A new approach to studying sponge cake aroma after storage in treated paper and plastic packaging by direct gas chromatography–olfactometry (D-GC–O)

2007

The objective of this study was to use D-GC–O to compare the global odour of a sponge cake flavoured with either a ‘viennoiserie’ aromatic note or a simplified mixture of aroma compounds (used for physicochemical studies), then stored in a glass packaging (inert and impermeable) or in pouches made with treated papers or with plastic packaging, in accelerated ageing conditions (high temperature and relative humidity gradient). After 1 week of storage, the flavoured sponge cake headspace was SPME-extracted directly into the packaging and analysed by D-GC–O. The sponge cake global odour was better retained if plastic film rather than treated-papers was used, for both flavourings. Changes in th…

Comments on “Finite-Time $H_{\infty }$ Fuzzy Control of Nonlinear Jump Systems With Time Delays Via Dynamic Observer-Based State Feedback”

2014

This paper investigates a defect appearing in “Finite-time H∞ fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback,” which the observer-based finite-time H∞ controller via dynamic observer-based state feedback could not ensuring stochastic finite-time boundedness, and satisfying a prescribed level of H∞ disturbance attenuation for the resulting closed-loop error fuzzy Markov jump systems. The corrected results are presented, and the improved optimal algorithms and new simulation results are also provided in this paper.

Observer-based stabilization of spacecraft rendezvous with variable sampling and sensor nonlinearity

2013

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/902452 Open Access This paper addresses the observer-based control problem of spacecraft rendezvous with nonuniform sampling period. The relative dynamic model is based on the classical Clohessy-Wiltshire equation, and sensor nonlinearity and sampling are considered together in a unified framework. The purpose of this paper is to perform an observer-based controller synthesis by using sampled and saturated output measurements, such that the resulting closed-loop system is exponentially stable. A time-dependent Lyapunov functional is devel…

2014

State estimation problem is considered for a kind of wireless network control system with stochastic uncertainty and time delay. A sliding mode observer is designed for the system under the situation that no missing measurement occurs and system uncertainty happens in a stochastic way. The observer designed for the system can guarantee the system states will be driven onto the sliding surface under control law, and the sliding motion of system states on sliding surface will be stable. By constructing proper Lyapunov-Krasovskii functional, sufficient conditions are acquired via linear matrix inequality. Finally, simulation result is employed to show the effectiveness of the proposed method.

Occurrence of fourteen mycotoxins in tiger-nuts

2012

Abstract A previous developed matrix solid-phase dispersion (MSPD) extraction method was applied for the routine analysis of aflatoxins (AFs), ochratoxin A (OTA), fumonisins (FB 1 and FB 2 ), beauvericin (BEA), nivalenol (NIV), deoxynivalenol (DON), the toxin T-2 (T-2), toxin HT-2 (HT-2), diacetoxyscirpenol (DAS) and zearalenone (ZEN) in tiger-nuts by liquid chromatography–triple-quadrupole linear ion trap (HPLC–QTRAP ® ). The extraction solid support used was C 18 , while the elution solvent was acetonitrile/methanol (50/50, v/v) 1 mM ammonium formate. Using matrix-matched calibration, recoveries and repeatabilities were in the range 67–89% and 2–11% relative standard deviation (RSD), resp…