fast decomposition of matrices generated by the boundary element method a new method to reduce the solution time of matrices generated by the boundary element method is presented here the method involves converting the fully populated system into a banded system by lumping certain coefficients of the matrix into fictitious nodes and then constraining these nodes to accurately represent each coefficient the major advantages of lumping over the substructuring method are that lumping can be applied to arbitrarily shaped geometries and infinite domain problems and that it preserves the diagonal dominance of the matrix it is shown here that the proposed algorithm reduces the rate of increase of solution time t of an n degree of freedom problem from t n3 to t n2 although the algorithm is for thermal problems its extension to mechanical problems is straightforward the procedure can easily be incorporated into existing boundary element based packages

adaptive mesh redistribution for a boundary element panel method in this paper we extend the concept of a grading function as introduced by carey and dinh2 in a one dimensional context to curved contours we then apply the idea to adaptive grid redistribution for a boundary element method to solve a model boundary value problem numerical results are included for a potential problem to demonstrate the effect of the redistribution scheme on the solution and the geometry of the domain

critical blowup and global existence numbers for a weakly coupled system of reaction diffusion equations let d rn be either all of rn or else a cone in rn whose vertex we may take to be at the origin without loss of generality let pi qj i 1 2 be nonnegative with 0 p1 q1 p2 q2 we consider the long time behavior of nonnegative solutions of the system u t delta u u p 1 v q 1 v t delta v u p 2 v q 2 s in d 0 with u0 v0 0 on d u v t x 0 0 0 t x u0 0 0 u0 0 e l d we obtain fujita type global existence global nonexistence theorems for s analogous to the classical result of fujita and others for the initial value problem for ut u up u x 0 u0 x 0 the principal result in the case d rn and p2q1 0 is that when p1 1 the system behaves like the single equation ut u up1vq1 with respect to fujita type blowup theorems whereas if p1 1 the behavior of the system is more complicated some of the results extend those of escobedo herrero when d rn and of levine when d is a cone these authors considered s in the case of p1 q2 0 an example of nonuniqueness is also given

boundary integral equations for recovery of design sensitivities in shape optimization a new formulation for obtaining design sensitivities in shape optimization has been developed the formulation is based on a direct application of the material derivative concept to the appropriate boundary integral equations for displacements and stresses in an elastic solid as a check on accuracy the approach was applied to a uniformly loaded infinite plate containing an elliptical hole in this case the availability of an analytical solution made it possible to calculate errors exactly furthermore a wide range of stress states could be considered simply by varying the aspect ratio of the elliptical hole for convenience the design sensitivities were calculated with respect to changes in the major axis numerical convergence was established by comparing results based on four successive boundary meshes in general the predictions for both displacement and stress sensitivities were remarkably accurate

semilinear reaction diffusion systems of several components abstract the homogeneous dirichlet boundary value problem u it u i j 1 n u j p ij i 1 2 n in a bounded domain r n is considered where p ij 0 1 i j n are constants denote by i the identity matrix and p pij which is assumed to be irreducible we find out that whether or not i p is a so called m matrix plays a fundamental role in the blow up theorems

p adaptive boundary elements this paper presents the implementation of an adaptive philosophy to plane potential problems using the direct boundary element method after some considerations about the state of the art and a discussion of the standard approach features the possibility of separately treating the modelling of variables and their interpolation through hierarchical shape functions is analysed then the proposed indicators and estimators are given followed by a description of a small computer program written for an ibm pc finally some examples show the kind of results to be expected

an iterative method for the boundary element solution of the exterior acoustic problem abstract in this paper we discuss the burton and miller s boundary integral formulation of the exterior neumann problem for the helmholtz equation which is uniquely solvable for all frequencies as well as a similar formulation of brakhage and werner lies and also panich for the exterior dirichlet problem we present an iterative procedure for the efficient solution of the full linear systems arising from the discretisation of such boundary integral equations numerical results will also be presented for the neumann problem for a class of axisymmetric ellipsoids

a note on the generalized conjugate gradient method each iterate generated by the generalized conjugate gradient method of concus and golub lecture notes in economics and mathematical systems 134 springer verlag new york 1976 and widlund siam j numer anal 15 1978 pp 801 812 is shown to be the best approximation to the solution from a certain affine subspace although not from the natural afline krylov subspace this property is used to improve the error bounds given by widlund and hageman luk and young siam j numer anal 17 1980 pp 852 873

boundary element methods for optimization of distributed parameter systems a numerical method of solution is proposed for optimization problems of distributed parameter systems two model problems from continuum mechanics are investigated by means of constructing the problems as the steady state optimal control problems governed by elliptic partial differential equations the basis of the suggested method of solution lies in the space discretization of the necessary conditions for optimality by the boundary element method and the minimization of the performance indices by the conjugate gradient method of optimization

adaptive h p and hp versions for boundary integral element methods recently very promising results in a so called hp version of the finite element method have been obtained the basic idea is a balanced combination of mesh refinement and increase of the polynomial degree of the shape functions this idea is applied to a boundary collocation method in this paper the new method is compared with adaptive h and p versions and it is shown in numerical examples that even in the presence of singularities in the exact solution exponential convergence is obtained

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

non simultaneous blow up for n componential parabolic systems abstract this paper deals with the non simultaneous and simultaneous blow up for some parabolic systems u i t u i u i p i coupled via nonlinear boundary flux u i u i 1 q i 1 i 1 2 n for radially symmetric solutions we obtain that one component can blow up by itself and may provide sufficient help to the blow up of the other k 0 1 n 2 ones under suitable initial data in particular such phenomena happen for every initial data in some exponent regions it is interesting that there exist initial data such that any two components blow up simultaneously either of which blows up depending on itself and also can give sufficient help to the other components blowing up simultaneously a necessary and sufficient condition is obtained on the simultaneous blow up of at least two components for all initial data moreover the non simultaneous and simultaneous blow up rates and sets are determined

iterative solution techniques in boundary element analysis iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis bea method are discussed continuum structural response analysis problems are considered employing single and multi zone boundary element models with and without zone condensation the impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices resulting in multi zone bea is studied both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods to characterize the potential of these iterative techniques we discuss accuracy storage and timing statistics in comparison with analogous information from direct sparse blocked matrix factorization procedures matrix populations that experience block fill in during the direct decomposition process are included with different degrees of preconditioning iterative equation solving is shown to be competitive with direct methods for the problems considered

blowup estimates for a semilinear reaction diffusion system this paper deals with the blowup estimates of positive solutions for a semilinear reaction diffusion system ut u u vp vt v uqv with null dirichlet boundary conditions the upper and lower bounds of blowup rates are obtained

blow up analysis for a system of heat equations with nonlinear flux which obey different laws abstract we consider a system of heat equations u t u and v t v in 0 t completely coupled by nonlinear boundary conditions u e p v u v u q e v on 0 t we prove that the solutions always blow up in finite time for non zero and non negative initial values also the blow up only occurs on with c 1 t t p 2 p q max u x t c 2 t t p 2 p q log c 3 t t q 1 2 p q max v x t log c 4 t t q 1 2 p q for p q 0 0 1 and 0 p

numerical solution of bernoulli type free boundary value problems by variable domain method the variable domain method for a free surface problem is considered as a weighted residual method this considerably simplifies discretization of the problem and at the same time allows implementation of any standard discretization technique discretization of the problem results in a non linear system of equations for discrete values of a field variable and co ordinates of the nodes on the free boundary variables corresponding to a field variable are eliminated and the resulting non linear system is of considerable smaller size some new update strategies of the jacobian together with discussion of the cost effectiveness and covergence rate are introduced and compared to broyden s method

a posteriori estimates of the solution error caused by discretization in the finite element finite difference and boundary element methods a theory is described which guarantees an upper and lower bound estimate of the discretization error in numerical solutions of elliptic boundary value problems this method gives bounded global estimates of the error in the energy norm pointwise estimates of the error in the solution variable or its derivatives can then be obtained if the numerical solution is exhibiting pointwise monotonic convergence the versatility of this method is illustrated by its application to numerical solutions from finite element finite difference and boundary element methods

incremental learning of 3d dct compact representations for robust visual tracking visual tracking usually requires an object appearance model that is robust to changing illumination pose and other factors encountered in video many recent trackers utilize appearance samples in previous frames to form the bases upon which the object appearance model is built this approach has the following limitations 1 the bases are data driven so they can be easily corrupted and 2 it is difficult to robustly update the bases in challenging situations in this paper we construct an appearance model using the 3d discrete cosine transform 3d dct the 3d dct is based on a set of cosine basis functions which are determined by the dimensions of the 3d signal and thus independent of the input video data in addition the 3d dct can generate a compact energy spectrum whose high frequency coefficients are sparse if the appearance samples are similar by discarding these high frequency coefficients we simultaneously obtain a compact 3d dct based object representation and a signal reconstruction based similarity measure reflecting the information loss from signal reconstruction to efficiently update the object representation we propose an incremental 3d dct algorithm which decomposes the 3d dct into successive operations of the 2d discrete cosine transform 2d dct and 1d discrete cosine transform 1d dct on the input video data as a result the incremental 3d dct algorithm only needs to compute the 2d dct for newly added frames as well as the 1d dct along the third dimension which significantly reduces the computational complexity based on this incremental 3d dct algorithm we design a discriminative criterion to evaluate the likelihood of a test sample belonging to the foreground object we then embed the discriminative criterion into a particle filtering framework for object state inference over time experimental results demonstrate the effectiveness and robustness of the proposed tracker

an iterative solution method for solving sparse nonsymmetiric linear systems abstract an algorithm is presented for the general solution of a set of linear equations ax b the method works exceptionally well for the solution of large sparse systems of linear equations the co efficient matrix a of which need not be symmetric but should have workable splits the method can be applied to problems which arise in convection diffusion flow of fluids and oil reservoir modeling the difference of the upper secondary diagonals super diagonals and the lower secondary diagonals sub diagonals of the matrix a leads to a decomposition of a into a difference of a symmetric matrix having the same lower structure as that of a and a strictly upper triangular matrix the symmetric matrix is made diagonally dominant and the system is solved iteratively

conforming boundary elements in plane elasticity for shape design sensitivity the structural design sensitivity analysis of a two dimensional continuum using conforming continuous boundary elements is investigated implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices a singular formulation of the boundary element method is used implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis the behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated a rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices thus avoiding the problems associated with their numerical integration a formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented the design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results numerical data comparing the performance of conforming and non conforming formulations in the calculation of design sensitivities are also presented the accuracy of the present results is demonstrated through comparisons with existing analytical results

global existence and blow up of solutions to a class of doubly degenerate parabolic equations coupled via nonlinear boundary flux the paper deals with the critical curve for a degenerate parabolic system coupled via nonlinear boundary flux by constructing the self similar super solution and subsolution we obtain the critical global existence curve and the critical curve of fujita type is conjectured with the aid of some new results an interesting feature of our results is that the critical global existence curve and the critical fujita curve are determined by a matrix and by the solution of a linear algebraic system respectively

solution of bem systems of equations via iterative techniques the present paper is concerned with the application of iterative techniques to solve boundary element method bem systems of equations initially a brief description of some algorithms which have been employed for symmetric positive definite matrices is given finite element method matrices for instance subsequently non symmetric versions of these algorithms are described and their performance is checked for bem matrices through various numerical experiments preconditioned algorithms were found to work quite well

optimal arrangement of holes in a two dimensional heat conductor by a special boundary integral method the position size and surface temperature of circular holes inside a two dimensional heat conductor are optimized to produce a minimum variation in surface temperature over a portion of the outer boundary this problem whic arises in thermal desing of moulds and dies resembles those encountered in structural shape optimization because the internal geometry of the heat conductor depends on the design variables in this paper some of the traditional difficulties associated with shape optimization are overcome by analysing steady heat conduction with a special boundary integral method developed for two dimensional regions with circular hole this approach eliminates the need to regenerate a finite element mesh over the interior of the region each time the geometry is changed during the design process it also increases the efficiency of the analysis by reducing the number of unknowns in the numerical discretization of the region since the objective function depends only on the boundary temperatures there is no need to determine temperatures in the interior the analysis method is applied to two problems arising in optimal thermal design of compression moulds these examples show that the number of holes choson for the design strongly affects their resulting optimal arrangement as well as the ultimate uniformity of the cavity surface temperature

an algorithm for 3 dimensional free surface problems in hydrodynamics a numerical algorithm is presented for the solution of 3 dimensional problems involving a fluid with a free surface the fluid is assumed to be ideal and the exact non linear boundary conditions are applied on the fluid surface the problem is formulated in terms of a singular integral equation which is discretized and the resulting algebraic equations solved by a newton process advantage is taken of the structure of the free surface conditions enabling a substantial reduction in the number of unknowns to be determined some sample computational results are presented and compared with the predictions of linearized theory

critical curves for fast diffusive non newtonian equations coupled via nonlinear boundary flux this paper deals with the critical curve for a nonlinear boundary value problem of a fast diffusive non newtonian system we first obtain the critical global existence curve by constructing the self similar supersolution and subsolution and then the critical fujita curve is conjectured with the aid of some new results

blow up rate for a semilinear reaction diffusion system abstract this paper deals with the blow up rate of positive solution to semilinear reaction diffusion system u1 t u1 u2p1 un 1 t un 1 unpn 1 un u1 u1pn with null dirichlet boundary conditions the upper and lower bounds of blow up rate were obtained

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

coupled diffusion systems with localized nonlinear reactions this paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit ui upii 1 x0 t i 1 k uk 1 u1 in 0 t with boundary conditions ui 0 on 0 t we show that the solution has a global blowup the exact rate of the blowup is obtained and we also derive the estimate of the boundary layer and on the asymptotic behavior of the solution in the boundary layer

solution of elasticity problems by a self adaptive mesh refinement technique for boundary element computation a self adaptive mesh refinement technique is developed for boundary element solutions of the two dimensional navier s equation the method is based on error reduction and applied on the element and global level to estimate the residual error associated with each mesh results for several problems employing constant two dimensional isotropic elastostatic boundary elements are presented

the importance of diagonal dominance in the iterative solution of equations generated from the boundary element method the unsymmetric matrix equations generated from the boundary element method bem can be solved iteratively with convergence to the correct solution guaranteed if the boundary element system of equations can be first transformed into an equivalent diagonally dominant system a transformation is presented which selectively annihilates terms in the coefficient matrix of the system ax b until an equivalent row diagonally dominant system if available is obtained the new row diagonally dominant system is well suited for use with jacobi and gauss seidel point iterative equation solvers the diagonal dominizing transformation presented in this work is not suitable for large systems of equations but is useful as a research tool for studying the importance of diagonal dominance in the iterative solution of equations generated from the bem a simple laplacian problem is used to examine the structure of the bem equations and to introduce the diagonal dominizing transformation the importance of diagonal dominance is shown by comparing iterative convergence of positive definite symmetric positive definite and diagonally dominant systems of bem equations obtained from a plane strain elasticity problem

the convergence of linear stationary iterative processes for solving singular unstructured systems of linear equations this paper reviews the convergence properties of linear stationary iterative processes for solving large unstructured systems of linear equations special attention is given to the case where the system to be solved is singular and possibly inconsistent the review starts by investigating the iteration bf x k 1 h bf x k bf f k 0 1 2 cdots when the system i h bf x bf f is inconsistent in this case the sequence left bf x k right always diverges nevertheless when h is convergent there exists a vector bf q in text null i h such that the sequence hat bf x k bf x k k bf q converges the limit of this sequence hat bf x solves a certain least squares problem and the sequence of residual vectors bf r k i h bf x k bf f converges to i h hat bf x bf f furthermore if h is similar to a real diagonal matrix then the corresponding norms of bf r k and hat bf x k hat bf x decr

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

blow up behaviors for semilinear parabolic systems coupled in equations and boundary conditions abstract this paper concerns with blow up behaviors for semilinear parabolic systems coupled in equations and boundary conditions in half space we establish the rate estimates for blow up solutions and prove that the blow up set is r n under proper conditions on initial data furthermore for n 1 more complete conclusions about such two topics are given

robust control based object tracking this correspondence presents a video tracking framework using control based observer design it unifies several kernel based approaches into a consistent theoretical framework by modeling tracking as a recursive inverse problem the framework relies on observability theory to handle the ldquosingularityrdquo problem and provides explicit criteria for kernel design and dynamics evaluation

a uniqueness result for a semilinear parabolic system abstract we prove that for nonnegative continuous bounded and nonzero initial data we have a unique solution of the reaction diffusion system described by three differential equations with non lipschitz nonlinearity we also find the set of all nonnegative solutions of the system when the initial data is zero and in the last section we briefly discuss a generalization of the theorem to a system of n equations

the lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems many powerful methods for solving systems of equations can be regarded as projection methods most of the projection methods known for solving linear systems are orthogonal projection methods but little attention has been given to the class of nonorthogonal or oblique projection methods which is particularly attractive for large nonsymmetric systems the purpose of the paper is to present some methods in the general setting of oblique projection methods and to give some theoretical results some experiments comparing the various algorithms are reported

boundedness and blow up for a semilinear reaction diffusion system abstract we consider the semilinear parabolic system s u t u p t u q where x rnn 1 t 0 and p q are positive real numbers at t 0 nonnegative continuous and bounded initial values u0 v0 x are prescribed the corresponding cauchy problem then has a nonnegative classical and bounded solution u t x v t x in some strip st 0 t r n 0 t sup t 0 u v remain bounded in s t we show in this paper that if 0 t so that solutions can be continued for all positive times when pq 1 and 1 pq 1 n 2 with max p q one has t for every nontrivial solution u v t is then called the blow up time of the solution under consideration finally if 1 pq 1 n 2 both situations coexist since some nontrivial solutions remain bounded in any strip s while others exhibit finite blow up times

blowup estimates for a parabolic system in a three species cooperating model abstract blowup estimates for solutions of a parabolic system which arises in a cooperating three species food chain model with homogeneous dirichlet boundary conditions are investigated the upper bound of blowup rate for any n and the lower bound of blowup rate for n 1 are obtained

analysis of free surface flows using isoparametric finite elements a theory for free surface flow using variable geometry finite elements is numerically modelled using isoparametric finite elements for the first time the resulting nonlinear equations are solved using the newton raphson method because a functional is used as the basis of the formulation the resulting equations are symmetrical the realistic problem of flow over a crump weir is solved for a large range of discharges

on critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition abstract in this paper we consider the system arraycolsep0 14em begin array rcl hskip2em rcl hskip2em c u t delta u v p v whereas if max n 2 there exist both global and nonglobal nonnegative solutions

error indicators for adaptive mesh refinement in the boundary element method a new approach in this paper a new approach to the development of a posteriori error indicators for the direct boundary element method bem is presented it takes advantage of a unique opportunity offered by the collocation bem that is the possibility of obtaining more than one numerical solution from a given boundary element mesh unlike other approaches the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution in order to test the capability of the proposed error indicators to actually control a selective mesh refinement process an h adaptive refinement strategy is also described together with the criteria for refinement and for the termination of the adaptive process full details on the whole numerical implementation for two dimensional problems are provided in particular there is described a direct method for the numerical evaluation of cauchy principal value integrals numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst

single point blow up for parabolic systems with exponential nonlinearities and unequal diffusivities abstract we study positive blowing up solutions of systems of the form u t 1 u e p v v t 2 v e q u with 1 2 0 and p q 0 we prove single point blow up for large classes of radially decreasing solutions this answers a question left open in a paper of friedman and giga 1987 where the result was obtained only for the equidiffusive case 1 2 and the proof depended crucially on this assumption

blow up estimates of the positive solution of a parabolic system this paper establishes the blow up estimates for the systems ut u 0 vt v 0 in br 0 t br rn with the nonlinear boundary conditions u um1vn1 and v um2vn2 on sr 0 t where 0 m1 1 m2 and 0 n2 1 n1 we prove that c t t 2 max u x t c t t 2 and c t t 2 max v x t c t t 2 under some monotonicity assumptions on the initial values where n1 n2 1 m2 m1 1 and n1m2 1 m1 1 n2

interactions among multi nonlinearities in a nonlinear diffusion system with absorptions and nonlinear boundary flux abstract this paper deals with a nonlinear diffusion system with inner absorptions and coupled nonlinear boundary conditions two parameters which solve an introduced matrix equation covering all the eight nonlinear exponents of the system are used to get a simple description for the interactions among the multi nonlinearities in the system blow up or not of the solutions is determined by the signs of the two parameters in order to obtain the critical properties of the solutions for the critical sign of the parameters some further analysis on the absorption coefficients and the geometry of is given in addition to the discussion for the eight nonlinear exponents in the system

boundary integral equation method for shape optimization of elastic structures a general method for shape design sensitivity analysis as applied to plane elasticity problems is developed with a direct boundary integral equation formulation using the material derivative concept and adjoint variable method the problem formulation is very general and a complete consideration is given to describing the boundary variation by including the tangential component of the velocity field the method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary the accuracy of the design sensitivity analysis is studied with a fillet and an elastic ring design problem among the several numerical implementations tested the second order boundary elements with a cubic spline representation of the moving boundary have shown the best accuracy a smooth characteristic function is found to be better than a plateau function for localization of the stress constraint optimal shapes for the two problems are presented to show numerical applications

blow up of solutions for nonlinear parabolic equation with nonlocal source and nonlocal boundary condition this paper is devoted to a nonlinear parabolic equation subject to nonlocal boundary condition and with nonlocal reaction source some criteria on this problem which determine whether the solutions blow up in a finite time or exist globally are given moreover the blow up rate estimates are also obtained