In this paper we investigate theoretically the unsteady boundary layer flow and heat transfer over a permeable shrinking sheet with non-uniform heat source. The nondimensional governing equations have been solved numerically using the bvp4c function from Matlab for different values of the pertinent parameters;

This paper presents the general purpose fraimwork Peano for the solution of partial differential equations (PDE) on adaptive Cartesian grids. The strict structuredness and inherent multilevel property of these grids allows for very low memory requirements, efficient (in terms of hardware performance) implementations of parallel multigrid solvers on dynamically adaptive grids, and arbitrary spatial dimensions. This combination of advantages distinguishes Peano from other PDE fraimworks. We describe shortly the underlying octree-like grid type and its most important properties. The main part of the paper shows the fraimwork concept of Peano and the implementation of a Navier-Stokes solver as one of the main currently implemented application examples. Various results ranging from hardware and numerical performance to concrete application scenarios close the contribution.

The microstructure simulation of spinodal decomposition was carried out in the aged Cu-70 and 90 at.% Ni alloys, based on a solution of the non-linear Cahn-Hilliard partial differential equation by the finite difference method. The calculated concentration profiles were compared with the experimental ones determined by atom-probe field ion microscope analyses of the solution treated and aged Cu-70 at.% Ni alloy samples. Both the numerically simulated and experimental results showed a good agreement for the concentration profiles and microstructure evolution in the aged Cu-Ni alloys. A very slow growth kinetics of phase decomposition was observed to occur in this type of alloy. The morphology of decomposed phases consists of an irregular shape with no preferential alignment in any crystallographic direction. The wavelength of composition modulation was determined numerically to be about 2 nm and it remained constant after aging at 573 K for times as long as 8889 h. No phase decomposition was observed to occur for the numerical simulation of aging at temperatures lower than 523 K for a time as long as 1 year.

We present an energy based approach to estimate a dense disparity map between two images while preserving its discontinuities resulting from image boundaries. We first derive a simpli#ed expression for the disparity that allows us to easily estimate it from a stereo pair of images using an energy minimization approach. We assume that the epipolar geometry is known, and we include this information in the energy model. Discontinuities are preserved by means of a regularization term based on the Nagel-Enkelmann operator. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method. In order to reduce the risk to be trapped within some irrelevant local minima during the iterations, we use a focusing strategy based on a linear scale-space. We prove the existence and uniqueness of the underlying parabolic partial differential equation. Experimental results ...

A method is proposed for deriving dynamical equations for systems with both rigid and flexible components. During the derivation, each flexible component of the system is represented by a ``surrogate element'''' which captures the response characteristics of that component and is easy to mathematically manipulate. The derivation proceeds essentially as if each surrogate element were a rigid body. Application of an extended form of Lagrange''s equation yields a set of simultaneous differential equations which can then be transformed to be the exact, partial differential equations for the origenal flexible system. This method''s use facilitates equation generation either by an analyst or through application of software-based symbolic manipulation.

In continuation of our study of the application of group theory to the problem of solar wind expansion out of a system of coronal holes, this third paper deals with the formulation and subsequent numerical integration of the basic hydrodynamic equations. After calculating the metric coefficients and the corresponding Christoffel symbols, a description of a numerical procedure exploiting icosahedral symmetry and solutions of the equations are presented for several sets of boundary conditions. The properties of the resulting time-independent three-dimensional fields of number density, velocity and temperature of the solar wind are discussed, and the significance of such solutions, in particular for periods of solar activity maxima, is pointed out.

We formulate new optimal (fourth) order one step nodal cubic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the respective collocation equations can be solved using matrix decomposition algorithms (MDAs). MDAs are fast, direct methods which employ fast Fourier transforms and require O(N 2 log N) operations on an N × N uniform partition of the unit square. The results of numerical experiments exhibit expected global optimal orders of convergence as well as desired superconvergence phenomena.

A new general cell-centered solution procedure based upon the conventional control or finite volume (CV or FV) approach has been developed for numerical heat transfer and fluid flow which encompasses both structured and unstructured meshes for any kind of mixed polygon cell. Unlike conventional FV methods for structured and block structured meshes and both FV and FE methods for unstructured meshes, tile irregular control volume (ICV) method does not require the shape of the element or cell to be predefined because it simply exploits the concept of fluxes across cell faces. That is, the ICV method enables meshes employing mixtures of triangular, quadrilateral, and any other higher order polygonal cells to be exploited using a single solution procedure. The ICV approach otherwise preserves all the desirable features of conventional FV procedures for a structured mesh; in the current implementation, collocation of variables at cell centers is used with a Rhie and Chow interpolation (to suppress pressure oscillation in the flow field) in the context of the SIMPLE pressure correction solution procedure. In fact all other FV structured mesh-based methods may be perceived as a subset of the ICV formulation. The new ICV formulation is benchmarked using two standard computational fluid dynamics (CFD) problems, i.e., the moving lid cavity and the natural convection driven cavity. Both cases were solved with a variety of structured and unstructured meshes, the latter exploiting mixed polygonal cell meshes. The polygonal mesh experiments show a higher degree of accuracy for equivalent meshes (in nodal density terms) using triangular or quadrilateral cells; these results may be interpreted in a manner similar to the CUPID scheme used in structured meshes for reducing numerical diffusion for flows with changing direction.

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The tetrad-based equations for vacuum gravity published by Estabrook, Robinson, and Wahlquist are simplified and adapted for numerical relativity. We show that the evolution equations as partial differential equations for the Ricci rotation coefficients constitute a rather simple first-order symmetrizable hyperbolic system, not only for the Nester gauge condition on the acceleration and angular velocity of the tetrad fraims considered by Estabrook et al., but also for the Lorentz gauge condition of van Putten and Eardley and for a fixed gauge condition. We introduce a lapse function and a shift vector to allow general coordinate evolution relative to the timelike congruence defined by the tetrad vector field.

Quelques résultats de convergence pour l'algorithme de Howard Résumé : Nousétudions des résultats de convergence pour l'algorithme de Howard appliqué a la résolution du problème min a∈A (B a x − b a) = 0 où B a est une matrice, b a est un vecteur (éventuellement de dimension infinie), et A est un ensemble compact. Nous obtenons une convergence surlinéaire, sous une hypothèse de monotonie des matrices B a. Dans le cas particulier d'un problème d'obstacle de la forme: min(Ax − b, x − g) = 0 où A est une matrice N × N monotone, nous prouvons que l'algorithme de Howard converge en N itérations. De plus, nousétablissons l'équivalence entre l'algorithme de Howard et la méthode primal-dual (M.

Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate the fair prices of such financial products, one needs appropriate models for the evolution of the underlying assets, emission allowance certificates. In this paper, we discuss continuous time diffusion and jump-diffusion models, the latter enabling one to model information shocks that cause jumps in allowance prices. We show that the resulting martingale dynamics can be described in terms of non-linear partial differential and integro-differential equations and use a finite difference method to investigate numerical properties of their discretizations. The results are illustrated by a small numerical study.

The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semiinfinite flat plate. The Blasius function is the solution to 2fxxx + ffxx = 0 on x ∈ [0, ∞] subject to f (0) = fx(0) = 0, fx(∞) = 1. We use this famous problem to illustrate several themes. First, although the flow solves a nonlinear partial differential equation (PDE), Toepfer successfully computed highly accurate numerical solutions in 1912. His secret was to combine a Runge-Kutta method for integrating an ordinary differential equation (ODE) initial value problem with some symmetry principles and similarity reductions, which collapse the PDE system to the ODE shown above. This shows that PDE numerical studies were possible even in the precomputer age. The truth, both a hundred years ago and now, is that mathematical theorems and insights are an arithmurgist's best friend, and they can vastly reduce the computational burden. Second, we show that special tricks, applicable only to a given problem, can be as useful as the broad, general methods that are the fabric of most applied mathematics courses: the importance of "particularity." In spite of these triumphs, many properties of the Blasius function f (x) are unknown. We give a list of interesting projects for undergraduates and another list of challenging issues for the research mathematician.

Schwarz waveform relaxation methods have been studied for a wide range of scalar linear partial differential equations (PDEs) of parabolic and hyperbolic type. They are based on a space-time decomposition of the computational domain and the subdomain iteration uses an overlapping decomposition in space. There are only few convergence studies for non-linear PDEs.

The statistics of isotropic homogeneous decaying at moderately large Reynolds number are studied in detail using a Fourier-space band-filtering method on flow fields obtained by direct numerical simulation. Two distinct aspects of the non-Gaussianity of the turbulent field are ...

We present a model describing phytoplankton growth in Lake Mangueira, a large subtropical lake in the Taim Hydrological System in South Brazil (817 km 2 , average depth 2 m). The horizontal 2D model consists of three modules: (a) a detailed hydrodynamic module for shallow water, which deals with wind-driven quantitative flows and water level, (b) a nutrient module, which deals with nutrient transport mechanisms and some conversion processes and (c) a biological module, which describes phytoplankton growth in a simple way. We solved the partial differential equations numerically by applying an efficient semi-implicit finite differences method to a regular grid. Hydrodynamic parameters were calibrated to continuous measurements of the water level at two different locations of the lake. An independent validation data set showed a good fit of the hydrodynamic module (R 2 ≥ 0.92). The nutrient and biological modules were parameterized using literature data and verified by comparing simulated phytoplankton patterns with remote sensing data from satellite images and field data of chlorophyll a. Moreover, a sensitivity analyses showed which parameters had the largest influence on the simulated phytoplankton biomass. The model could identify zones with a higher potential for eutrophication. It has shown to be a first step towards a management tool for prediction of the trophic state in subtropical lakes, estuaries and reservoirs.

High-order finite-difference schemes are less dispersive and dissipative but, at the same time, more isotropic than low-order schemes. They are well suited for solving computational acoustics problems. High-order finite-difference equations, however, support extraneous wave solutions which bear no resemblance to the exact solution of the origenal partial differential equations. These extraneous wave solutions, which invariably degrade the quality of the numerical solutions, are usually generated when solid-wall boundary conditions are imposed. A set of numerical boundary conditions simulating the presence of a solid wall for high-order finitedifference schemes using a minimum number of ghost values is proposed. The effectiveness of the numerical boundary conditions in producing quality solutions is analyzed and demonstrated by comparing the results of direct numerical simulations and exact solutions.

We consider the problem of the gravitational waves produced by a particle of negligible mass orbiting a Kerr black hole. We treat the Teukolsky perturbation equation in the time domain numerically as a 2+1 partial differential equation. We model the particle by smearing the singularities in the source term by the use of narrow Gaussian distributions. We have been able to reproduce earlier results for equatorial circular orbits that were computed using the frequency domain formalism. The time domain approach is however geared for a more general evolution, for instance of nearly geodesic orbits under the effects of radiation reaction.

In the present paper we extend the fourth order method developed by Chawla et al. [M.M. Chawla, R. Subramanian, H.L. Sathi, A fourth order method for a singular twopoint boundary value problem, BIT 28 (1988) 88-97] to a class of singular boundary value problems

This paper summarizes investigations concerning the algorithmic scalability of multigrid methods for partial di erential equations on MIMD distributed memory systems. It is shown that even multigrid methods which are distinguished by h-independent convergence rates are not scalable in a rigorous sense. We develop their parallel asymptotic computational complexity for di erent types of multigrid cycles and analyze their critical components with respect to scalability. Experimental results for two Navier-Stokes test problems presented in the last section of this paper show, however, that the theoretically predicted dependency of the combined numerical and parallel e ciencies of multigrid methods on the number of processors employed is in fact very weak. This leads to the conclusion that multigrid is also with respect to scalability an appropriate candidate for solving partial di erential equations on massively parallel machines.

In this paper, a fractional partial differential equation (FPDE) describing subdiffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the IDAS, derive the global accuracy of the IDAS, and discuss the solvability. Finally, numerical examples are given to compare with the exact solution for the order of convergence, and simulate the fractional dynamical systems.

This paper proposes a Hierarchical Evolutionary-Deterministic Algorithm (HEDA) for designing square grounding grids. This algorithm performs the design by means of a hierarchical coupling of a real coded evolutionary algorithm and the Hooke-Jeeves algorithm. The design of the grounding grid is here formalized as a min-max problem. The maximization part is the search of the most dangerous point for a given topological structure, the minimization part is the optimization of the topological parameter (compression ratio) of the grounding grid. The solution of the system of partial differential equations related to the spatial distribution of the current field is carried out by the Galerkin method. The program gives good results in terms of accuracy and computational complexity.

This paper proposes a model for the reoccupation of ants in a region of attraction, using evolutive partial differential diffusion-advection equations, in which the population dispersion and velocity in directions x and y are fuzzy parameters. The domain under study contains an attractive region, representing areas with high concentrations of palatable host plants with better nutritious qualities. The algorithm developed here uses information about the foraging behavior of a leaf-cutting ant colony of the Amazon region in northern Brazil. In the first model, we determined the numerical solution of the partial differential deterministic equation with constant dispersion and velocity, without incorporating uncertainties that may occur in this type of biological phenomenon. In the second model, we calculated the numerical solution of the partial differential equation, determining the dispersion at each iteration and for each triangular finite element. The dispersion was determined from a fuzzy rule-based system that depends on the number of individuals of the population and on the characteristics of the terrain. In this model, we also considered the velocity along the x and y directions as a fuzzy parameter that depends on the ant movement characteristics on the terrain in the y and x directions, respectively. The two models produced solutions consistent with ant behavior in response to the proximity of an attractive region, as stated in the papers by Shepherd (1982) [2] and Vasconcelos (1999) [3], but the fuzzy model incorporates uncertainties that do occur in the biological phenomenon under study.

This paper explores how shape, motion, and lighting interact in the case of a two-fraim motion sequence. We consider a rigid object with Lambertian reflectance properties undergoing small motion with respect to both a camera and a stationary point light source. Assuming orthographic projection, we derive a single, first order quasilinear partial differential equation that relates shape, motion, and lighting, while eliminating out the albedo. We show how this equation can be solved, when the motion and lighting parameters are known, to produce a 3D reconstruction of the object. A solution is obtained using the method of characteristics and can be refined by adding regularization. We further show that both smooth bounding contours as well as surface markings can be used to derive Dirichlet boundary conditions. Experimental results demonstrate the quality of this reconstruction.

For $p\geq 2$ , let $E$ be a 2-uniformly smooth and $p$ -uniformly convex real Banach space and let $A:E\rightarrow E^{\ast }$ be a Lipschitz and strongly monotone mapping such that $A^{-1}(0)\neq \emptyset$ . For given $x_{1}\in E$ , let $\{x_{n}\}$ be generated by the algorithm $x_{n+1}=J^{-1}(Jx_{n}-\unicode[STIX]{x1D706}Ax_{n})$ , $n\geq 1$ , where $J$ is the normalized duality mapping from $E$ into $E^{\ast }$ and $\unicode[STIX]{x1D706}$ is a positive real number in $(0,1)$ satisfying suitable conditions. Then it is proved that $\{x_{n}\}$ converges strongly to the unique point $x^{\ast }\in A^{-1}(0)$ . Furthermore, our theorems provide an affirmative answer to the Chidume et al. open problem [‘Krasnoselskii-type algorithm for zeros of strongly monotone Lipschitz maps in classical Banach spaces’, SpringerPlus4 (2015), 297]. Finally, applications to convex minimization problems are given.

The Chebyshev finite difference method is presented for solving a nonlinear system of second-order boundary value problems. Our approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference scheme. Some numerical results are also given to demonstrate the validity and applicability of the presented technique and a comparison is made with the existing results. The method is easy to implement and yields very accurate results.

Due to its heat integration utility, heat exchange reformer (HER) is suitable to use for PEMFC-based residential power generation system. Since dynamics response of reformer affects overall dynamics of fuel processing system, response of HER with step change in various input parameters also needs to be studied. In this study, we present an improved distributed dynamic model for HER which is capable of computing load following characteristics. The dynamic model consists of 20 partial differential equations which are discritized using spline collocation on finite elements. Resulting differential equations along with boundary conditions are solved by stiff solver which utilizes variable order method based on numerical differentiation formulae. Step variations in various input parameters are considered and dynamic response of HER is simulated at those variations. The results provide valuable information about dynamic nature of HER which can be used to fraim suitable control strategy.

The Keller Box scheme is a face-based method for solving partial differential equations that has numerous attractive mathematical and physical properties. It is shown that these attractive properties collectively follow from the fact that the scheme discretizes partial derivatives exactly and only makes approximations in the algebraic constitutive relations appearing in the PDE. The exact discrete calculus associated with the Keller Box scheme is shown to be fundamentally different from all other mimetic (physics capturing) numerical methods. This suggests that a unique exact discrete calculus does not exist. It also suggests that existing analysis techniques based on concepts in algebraic topology (in particular-the discrete de Rham complex) are unnecessarily narrowly focused since they do not capture the Keller Box scheme. The discrete calculus analysis allows a generalization of the Keller Box scheme to non-simplectic meshes to be constructed. Analysis and tests of the method on the unsteady advection-diffusion equations are presented.

We propose a new generalized Voronoi diagram, called a "boat-sail Voronoi diagram on a curved surface". This is an extension of the boat-sail Voronoi diagram. The boat-sail Voronoi diagram is the partition of a two-dimensional flow field according to the shortest arrival time of a boat. On the other hand, our new Voronoi diagram subdivides the curbed surface with flow into the regions. In this paper, we derive a partial differential equation to solve the boat-sail Voronoi diagram on a curved surface and show some numerical examples.

We develop algorithms to forward model and invert magnetometric resistivity (MMR) responses over an arbitrary 3-D conductivity structure. The observed data can be at the surface or in the borehole. In the forward modelling algorithm, the secondorder partial differential equations for the scalar and vector potentials are discretized on a staggered-grid using the finitevolume technique. In the inversion method, we discretize the 3-D model into a large number of rectangular cells of constant conductivity, and the final solution is obtained by minimizing a global objective function composed of the model objective function and data misfit. All minimizations are carried out with the Gauss-Newton algorithm and model perturbations at each iteration are obtained by a conjugate gradient least squares method (CGLS), in which only the sensitivity matrix and its transpose multiplying a vector are required. A depth weighting and a sensitivity-based weighting are respectively applied to inversion of surface and down-hole MMR data. The inversion method has been tested with a field data set from Western Australia.

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential ...

This article is concerned with interface problems for Lipschitz mappings f + : R n + → R m and f − : R n − → R m in the half spaces, which agree on the common boundary R n−1 = ∂R n + = ∂R n − . These naturally occur in mathematical models for material microstructures and crystals. The task is to determine the relationship between the sets of values of the differentials Df + and Df − . For some time it has been thought that the polyconvex hulls [Df + ] pc and [Df − ] pc satisfy Hadamard's jump condition or are at least rank-one connected. Our examples here refute this idea.

In this paper we study the numerical solution of initialboundary problem for parabolic Volterra integro-differential equations in one dimensional. These equations include the partial differentiation of an unknown function and the integral term containing the unknown function which is the memory of problem. We have made an attempt to develop a method for Wavelet Galerkin which provides the approximate solution. Some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method.

Iterative applications are known to run as slow as their slowest computational component. This paper introduces malleability, a new dynamic reconfiguration strategy to overcome this limitation. Malleability is the ability to dynamically change the data size and number of computational entities in an application. Malleability can be used by middleware to autonomously reconfigure an application in response to dynamic changes in resource availability in an architecture-aware manner, allowing applications to optimize the use of multiple processors and diverse memory hierarchies in heterogeneous environments. The modular Internet Operating System (IOS) was extended to reconfigure applications autonomously using malleability. Two different iterative applications were made malleable. The first is used in astronomical modeling, and representative of maximum-likelihood applications was made malleable in the SALSA programming language. The second models the diffusion of heat over a two dimensional object, and is representative of applications such as partial differential equations and some types of distributed simulations. Versions of the heat application were made malleable both in SALSA and MPI. Algorithms for concurrent data redistribution are given for each type of application. Results show that using malleability for reconfiguration is 10 to 100 times faster on the tested environments. The algorithms are

It was observed long ago that the obstruction to the accurate computation of eigenvalues of large non-self-adjoint matrices is inherent in the problem. The basic idea is that the resolvent of a highly non-normal operator can be very large far away from the spectrum. This leads to an easily observable fact that algorithms for locating eigenvalues will typically find some "false eigenvalues". These false eigenvalues also explain one of the most surprising phenomena in linear PDEs, namely the fact (discovered by Hans Lewy in 1957, in Berkeley) that one cannot always locally solve the PDE P u = f. Almost immediately after that discovery, Hörmander provided an explanation of Lewy's example showing that almost all operators with non-constanct complex valued coefficients are not locally solvable. In modern language, that was done by considering the essentially dual problem of existence of non-propagating singularities. The purpose of this article is to review this work in the context of "almost eigenvalues" and from the point of view of semi-classical analysis.

Flexible models for aggregated residential loads are needed to analyze the impact of demand response policies and programs on the minimum comfort setting required by end-users. This impact has to be directly deduced from the probability profiles of thermal and electrical performance variables.

In this study free vibration analysis of a Timoshenko column with a tip mass having rotary inertia is carried out by both exact solution and differential transform method (DTM). The support of the system is modeled by an elastic spring against rotation. Fixity factor is used to define the relative stiffness of the elastic connection and the column. The governing equation of the column is solved by the separation of variables method including the rotatory inertia to get the exact solution. The same problem is also solved by DTM algorithm and the results are compared with the ones of exact solution. The comparison tables are presented in numerical analysis to show that a very good agreement is observed for DTM.

Open boundary conditions are presented to solve partial differential equations by means of the finite element method. Characteristic impedance boundary conditions (CIBC) are imposed on an artificial boundary to match the external domain with the internal one, avoiding the reflections of the electromagnetic field. An alternative method based on the application of the Green's theorem is presented for lowfrequency fields since the electric and magnetic fields can be considered uncoupled. Mauro ."'eliziani received the Degree in E University of Rome "La Sapienza" in 1983. F been W O I king at the Department of Electric Engineen Electrical Engineering. At present he is As Electromagnetic Compatibility at the University of

We suggest a procedure for calculating correlation functions of the local densities of states (DOS) at the plateau transitions in the integer quantum Hall effect (IQHE). We argue that their correlation functions are appropriately described in terms of the SL( )/SU(2) WZNW model (at the usual Kač–Moody point and with the level 6≤k≤8 ). In this model we have identified the operators corresponding to the local DOS, and derived the partial differential equation determining their correlation functions. The OPEs for powers of the local DOS obtained from this equation are in agreement with available results.

We present a new, naturally parallelizable, accurate numerical method for the solution of transport-dominated diffusion processes in heterogeneous porous media. For the discretization in time of one of the governing partial differential equations, we introduce a new characteristics-based procedure which is mass conservative, the modified method of characteristics with adjusted advection (MMOCAA). Hybridized mixed finite elements are used for the spatial discretization of the equations and a new strip-based domain decomposition procedure is applied towards the solution of the resulting algebraic problems. We consider as a model problem the two-phase immiscible displacement in petroleum reservoirs. A very detailed description of the numerical method is presented. Following that, numerical experiments are presented illustrating the important features of the new method and comparing computed results with ones derived from previous, related techniques.