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Accurate Schemes (accurate + scheme)
Selected AbstractsMolecular versatility of antibodiesIMMUNOLOGICAL REVIEWS, Issue 1 2002Henry Metzger Summary: As immunology developed into a discrete discipline, the principal experimental efforts were directed towards uncovering the molecular basis of the specificity exhibited by antibodies and the mechanism by which antigens induced their production. Less attention was given to how antibodies carry out some of their effector functions, although this subject presents an interesting protein-chemical and evolutionary problem; that is, how does a family of proteins that can bind a virtually infinite variety of ligands, many of which the species producing that protein has never encountered, reproducibly initiate an appropriate response? The experimental data persuasively suggested that aggregation of the antibody was a necessary and likely sufficient initiating event, but this only begged the question: how does aggregation induce a response? I used the IgE:mast cell system as a paradigm to investigate this subject. Data from our own group and from many others led to a molecular model that appears to explain how a cell ,senses' that antigen has reacted with the IgE. The model is directly applicable to one of the fundamental questions cited above, i.e. the mechanism by which antigens induce the production of antibodies. Although the model is conceptually simple, incorporating the actual molecular events into a quantitatively accurate scheme represents an enormous challenge. [source] An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction integral and micromechanics modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Jeong-Ho Kim Abstract The interaction integral is a conservation integral that relies on two admissible mechanical states for evaluating mixed-mode stress intensity factors (SIFs). The present paper extends this integral to functionally graded materials in which the material properties are determined by means of either continuum functions (e.g. exponentially graded materials) or micromechanics models (e.g. self-consistent, Mori,Tanaka, or three-phase model). In the latter case, there is no closed-form expression for the material-property variation, and thus several quantities, such as the explicit derivative of the strain energy density, need to be evaluated numerically (this leads to several implications in the numerical implementation). The SIFs are determined using conservation integrals involving known auxiliary solutions. The choice of such auxiliary fields and their implications on the solution procedure are discussed in detail. The computational implementation is done using the finite element method and thus the interaction energy contour integral is converted to an equivalent domain integral over a finite region surrounding the crack tip. Several examples are given which show that the proposed method is convenient, accurate, and computationally efficient. Copyright © 2003 John Wiley & Sons, Ltd. [source] High-order ENO and WENO schemes for unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2007W. R. Wolf Abstract This work describes the implementation and analysis of high-order accurate schemes applied to high-speed flows on unstructured grids. The class of essentially non-oscillatory schemes (ENO), that includes weighted ENO schemes (WENO), is discussed in the paper with regard to the implementation of third- and fourth-order accurate methods. The entire reconstruction process of ENO and WENO schemes is described with emphasis on the stencil selection algorithms. The stencils can be composed by control volumes with any number of edges, e.g. triangles, quadrilaterals and hybrid meshes. In the paper, ENO and WENO schemes are implemented for the solution of the dimensionless, 2-D Euler equations in a cell centred finite volume context. High-order flux integration is achieved using Gaussian quadratures. An approximate Riemann solver is used to evaluate the fluxes on the interfaces of the control volumes and a TVD Runge,Kutta scheme provides the time integration of the equations. Such a coupling of all these numerical tools, together with the high-order interpolation of primitive variables provided by ENO and WENO schemes, leads to the desired order of accuracy expected in the solutions. An adaptive mesh refinement technique provides better resolution in regions with strong flowfield gradients. Results for high-speed flow simulations are presented with the objective of assessing the implemented capability. Copyright © 2007 John Wiley & Sons, Ltd. [source] Towards very high-order accurate schemes for unsteady convection problems on unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005R. Abgrall Abstract We construct several high-order residual-distribution methods for two-dimensional unsteady scalar advection on triangular unstructured meshes. For the first class of methods, we interpolate the solution in the space,time element. We start by calculating the first-order node residuals, then we calculate the high-order cell residual, and modify the first-order residuals to obtain high accuracy. For the second class of methods, we interpolate the solution in space only, and use high-order finite difference approximation for the time derivative. In doing so, we arrive at a multistep residual-distribution scheme. We illustrate the performance of both methods on several standard test problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] Analysis of super compact finite difference method and application to simulation of vortex,shock interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2001Fu Dexun Abstract Turbulence and aeroacoustic noise high-order accurate schemes are required, and preferred, for solving complex flow fields with multi-scale structures. In this paper a super compact finite difference method (SCFDM) is presented, the accuracy is analysed and the method is compared with a sixth-order traditional and compact finite difference approximation. The comparison shows that the sixth-order accurate super compact method has higher resolving efficiency. The sixth-order super compact method, with a three-stage Runge,Kutta method for approximation of the compressible Navier,Stokes equations, is used to solve the complex flow structures induced by vortex,shock interactions. The basic nature of the near-field sound generated by interaction is studied. Copyright © 2001 John Wiley & Sons, Ltd. [source] Fast direct solver for Poisson equation in a 2D elliptical domainNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2004Ming-Chih Lai Abstract In this article, we extend our previous work M.-C. Lai and W.-C. Wang, Numer Methods Partial Differential Eq 18:56,68, 2002 for developing some fast Poisson solvers on 2D polar and spherical geometries to an elliptical domain. Instead of solving the equation in an irregular Cartesian geometry, we formulate the equation in elliptical coordinates. The solver relies on representing the solution as a truncated Fourier series, then solving the differential equations of Fourier coefficients by finite difference discretizations. Using a grid by shifting half mesh away from the pole and incorporating the derived numerical boundary value, the difficulty of coordinate singularity can be elevated easily. Unlike the case of 2D disk domain, the present difference equation for each Fourier mode is coupled with its conjugate mode through the numerical boundary value near the pole; thus, those two modes are solved simultaneously. Both second- and fourth-order accurate schemes for Dirichlet and Neumann problems are presented. In particular, the fourth-order accuracy can be achieved by a three-point compact stencil which is in contrast to a five-point long stencil for the disk case. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 72,81, 2004 [source] | ||||||||||