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Boundary Integral Equations (boundary + integral_equation)
Selected AbstractsBoundary integral equations for two-dimensional low Reynolds number flow past a porous bodyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2009Mirela Kohr Abstract In this paper we use the method of matched asymptotic expansions in order to study the two-dimensional steady flow of a viscous incompressible fluid at low Reynolds number past a porous body of arbitrary shape. One assumes that the flow inside the porous body is described by the Brinkman model, i.e. by the continuity and Brinkman equations, and that the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. By considering some indirect boundary integral representations, the inner problems are reduced to uniquely solvable systems of Fredholm integral equations of the second kind in some Sobolev or Hölder spaces, while the outer problems are solved by using the singularity method. It is shown that the force exerted by the exterior flow on the porous body admits an asymptotic expansion with respect to low Reynolds number, whose terms depend on the solutions of the abovementioned system of boundary integral equations. In addition, the case of small permeability of the porous body is also treated. Copyright © 2008 John Wiley & Sons, Ltd. [source] A relation between the logarithmic capacity and the condition number of the BEM-matricesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2007W. Dijkstra Abstract We establish a relation between the logarithmic capacity of a two-dimensional domain and the solvability of the boundary integral equation for the Laplace problem on that domain. It is proved that when the logarithmic capacity is equal to one the boundary integral equation does not have a unique solution. A similar result is derived for the linear algebraic systems that appear in the boundary element method. As these systems are based on the boundary integral equation, no unique solution exists when the logarithmic capacity is equal to one. Hence, the system matrix is ill-conditioned. We give several examples to illustrate this and investigate the analogies between the Laplace problem with Dirichlet and mixed boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Electrostatic BEM for MEMS with thin beamsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2005Zhongping Bao Abstract Micro-electro-mechanical (MEM) and nano-electro-mechanical (NEM) systems sometimes use beam- or plate-shaped conductors that can be very thin,with h/L,,,(10,2,10,3) (in terms of the thickness h and length L of a beam or the side of a square pate). Conventional boundary element method (BEM) analysis of the electric field in a region exterior to such thin conductors can become difficult to carry out accurately and efficiently,especially since MEMS analysis requires computation of charge densities (and then surface tractions) separately on the top and bottom surfaces of such objects. A new boundary integral equation (BIE) is derived in this work that, when used together with the standard BIE with logarithmically singular kernels, results in a powerful technique for the BEM analysis of such problems with thin beams. This new approach, in fact, works best for very thin beams. This thin beam BEM is derived and discussed in this work. Copyright © 2005 John Wiley & Sons, Ltd. [source] P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003Emmanuel Perrey-Debain Abstract The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd. [source] Local discretization error bounds using interval boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009B. F. Zalewski Abstract In this paper, a method to account for the point-wise discretization error in the solution for boundary element method is developed. Interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented. The developed method does not assume any special properties besides the Laplace equation being a linear elliptic partial differential equation whose Green's function for an isotropic media is known. Numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error. Copyright © 2008 John Wiley & Sons, Ltd. [source] Meshless analysis of potential problems in three dimensions with the hybrid boundary node methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2004Jianming Zhang Abstract Combining a modified functional with the moving least-squares (MLS) approximation, the hybrid boundary node method (Hybrid BNM) is a truly meshless, boundary-only method. The method may have advantages from the meshless local boundary integral equation (MLBIE) method and also the boundary node method (BNM). In fact, the Hybrid BNN requires only the discrete nodes located on the surface of the domain. The Hybrid BNM has been applied to solve 2D potential problems. In this paper, the Hybrid BNM is extended to solve potential problems in three dimensions. Formulations of the Hybrid BNM for 3D potential problems and the MLS approximation on a generic surface are developed. A general computer code of the Hybrid BNM is implemented in C++. The main drawback of the ,boundary layer effect' in the Hybrid BNM in the 2D case is circumvented by an adaptive face integration scheme. The parameters that influence the performance of this method are studied through three different geometries and known analytical fields. Numerical results for the solution of the 3D Laplace's equation show that high convergence rates with mesh refinement and high accuracy are achievable. Copyright © 2004 John Wiley & Sons, Ltd. [source] Two-dimensional unsteady heat conduction analysis with heat generation by triple-reciprocity BEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2001Yoshihiro Ochiai Abstract If the initial temperature is assumed to be constant, a domain integral is not needed to solve unsteady heat conduction problems without heat generation using the boundary element method (BEM).However, with heat generation or a non-uniform initial temperature distribution, the domain integral is necessary. This paper demonstrates that two-dimensional problems of unsteady heat conduction with heat generation and a non-uniform initial temperature distribution can be solved approximately without the domain integral by the triple-reciprocity boundary element method. In this method, heat generation and the initial temperature distribution are interpolated using the boundary integral equation. Copyright © 2001 John Wiley & Sons, Ltd. [source] Diffraction of light revisitedMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2008Matthias Kunik Abstract The diffraction of monochromatic light is considered for a plane screen with an open infinite slit by solving the vectorial Maxwell,Helmholtz system in the upper half-space with the Fourier method. With this approach we can represent each solution satisfying an appropriate energy condition by its boundary fields in the Sobolev spaces H±1/2. We show that Sommerfeld's theory using a boundary integral equation with Hankel kernels for the so-called B-polarization is covered by our approach, but in general it violates a necessary energy condition. Our representation includes also solutions which are not covered by Sommerfeld's theory. Copyright © 2007 John Wiley & Sons, Ltd. [source] On the stability and convergence of the finite section method for integral equation formulations of rough surface scatteringMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2001A. Meier We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces. Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A,, of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ,flattened' in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd. [source] The boundary integral equation approach for numerical solution of the one-dimensional Sine-Gordon equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2008Mehdi Dehghan Abstract This article describes a numerical method based on the boundary integral equation and dual reciprocity method for solving the one-dimensional Sine-Gordon (SG) equation. The time derivative is approximated by the time-stepping method and a predictor,corrector scheme is employed to deal with the nonlinearity which appears in the problem. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach. In addition, the conservation of energy in SG equation is investigated. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source] Time domain 3D fundamental solutions for saturated poroelastic media with incompressible constituentsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2008Mohsen Kamalian Abstract This paper presents simple time domain fundamental solutions for the three-dimensional (3D) well known u,p formulation of saturated porous media, neglecting the compressibility of fluid and solid particles. At first, the corresponding boundary integral equations as well as the explicit Laplace transform domain fundamental solutions are obtained in terms of solid displacements and fluid pressure. Subsequently, the closed form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Finally, a set of numerical results are presented which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source] Three-dimensional elastoplastic analysis by triple-reciprocity boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2007Yoshihiro Ochiai Abstract In general, internal cells are required to solve elastoplastic problems using a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is ease of data preparation, is lost. Triple-reciprocity BEM can be used to solve two-dimensional elastoplasticity problems with a small plastic deformation. In this study, it is shown that three-dimensional elastoplastic problems can be solved, without the use of internal cells, by the triple-reciprocity BEM. An initial strain formulation is adopted and the initial strain distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solving several problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] An advanced boundary element method for solving 2D and 3D static problems in Mindlin's strain-gradient theory of elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010G. F. Karlis Abstract An advanced boundary element method (BEM) for solving two- (2D) and three-dimensional (3D) problems in materials with microstructural effects is presented. The analysis is performed in the context of Mindlin's Form-II gradient elastic theory. The fundamental solution of the equilibrium partial differential equation is explicitly derived. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative, is developed. The global boundary of the analyzed domain is discretized into quadratic line and quadrilateral elements for 2D and 3D problems, respectively. Representative 2D and 3D numerical examples are presented to illustrate the method, demonstrate its accuracy and efficiency and assess the gradient effect on the response. The importance of satisfying the correct boundary conditions in gradient elastic problems is illustrated with the solution of simple 2D problems. Copyright © 2010 John Wiley & Sons, Ltd. [source] Traffic flow continuum modeling by hypersingular boundary integral equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2010Luis M. Romero Abstract The quantity of data necessary in order to study traffic in dense urban areas through a traffic network, and the large volume of information that is provided as a result, causes managerial difficulties for the said model. A study of this kind is expensive and complex, with many sources of error connected to each step carried out. A simplification like the continuous medium is a reasonable approximation and, for certain dimensions of the actual problem, may be an alternative to be kept in mind. The hypotheses of the continuous model introduce errors comparable to those associated with geometric inaccuracies in the transport network, with the grouping of hundreds of streets in one same type of link and therefore having the same functional characteristics, with the centralization of all journey departure points and destinations in discrete centroids and with the uncertainty produced by a huge origin/destination matrix that is quickly phased out, etc. In the course of this work, a new model for characterizing traffic in dense network cities as a continuous medium, the diffusion,advection model, is put forward. The model is approached by means of the boundary element method, which has the fundamental characteristic of only requiring the contour of the problem to be discretized, thereby reducing the complexity and need for information into one order versus other more widespread methods, such as finite differences and the finite element method. On the other hand, the boundary elements method tends to give a more complex mathematical formulation. In order to validate the proposed technique, three examples in their fullest form are resolved with a known analytic solution. Copyright © 2009 John Wiley & Sons, Ltd. [source] Meshless thermo-elastoplastic analysis by triple-reciprocity boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Yoshihiro OchiaiArticle first published online: 18 SEP 200 Abstract In general, internal cells are required to solve thermo-elastoplasticity problems by a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the easy preparation of data, is lost. A conventional multiple-reciprocity boundary element method (MRBEM) cannot be used to solve elastoplasticity problems, because the distribution of initial strain or stress cannot be determined analytically. In this study, it is shown that without the use of internal cells, two-dimensional thermo-elastoplasticity problems can be solved by a triple-reciprocity BEM using a thin plate spline. Initial strain and stress formulations are adopted and the initial strain or stress distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solve several problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] An energy approach to space,time Galerkin BEM for wave propagation problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2009A. Aimi Abstract In this paper we consider Dirichlet or Neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential. Starting from a natural energy identity, a space,time weak formulation for 1D integral problems is briefly introduced, and continuity and coerciveness properties of the related bilinear form are proved. Then, a theoretical analysis of an extension of the introduced formulation for 2D problems is proposed, pointing out the novelty with respect to existing literature results. At last, various numerical simulations will be presented and discussed, showing unconditional stability of the space,time Galerkin boundary element method applied to the energetic weak problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] A hypersingular time-domain BEM for 2D dynamic crack analysis in anisotropic solidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2009M. Wünsche Abstract A hypersingular time-domain boundary element method (BEM) for transient elastodynamic crack analysis in two-dimensional (2D), homogeneous, anisotropic, and linear elastic solids is presented in this paper. Stationary cracks in both infinite and finite anisotropic solids under impact loading are investigated. On the external boundary of the cracked solid the classical displacement boundary integral equations (BIEs) are used, while the hypersingular traction BIEs are applied to the crack-faces. The temporal discretization is performed by a collocation method, while a Galerkin method is implemented for the spatial discretization. Both temporal and spatial integrations are carried out analytically. Special analytical techniques are developed to directly compute strongly singular and hypersingular integrals. Only the line integrals over an unit circle arising in the elastodynamic fundamental solutions need to be computed numerically by standard Gaussian quadrature. An explicit time-stepping scheme is obtained to compute the unknown boundary data including the crack-opening-displacements (CODs). Special crack-tip elements are adopted to ensure a direct and an accurate computation of the elastodynamic stress intensity factors from the CODs. Several numerical examples are given to show the accuracy and the efficiency of the present hypersingular time-domain BEM. Copyright © 2008 John Wiley & Sons, Ltd. [source] Explicit expressions for 3D boundary integrals in potential theory,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009S. Nintcheu Fata Abstract On employing isoparametric, piecewise linear shape functions over a flat triangular domain, exact expressions are derived for all surface potentials involved in the numerical solution of three-dimensional singular and hyper-singular boundary integral equations of potential theory. These formulae, which are valid for an arbitrary source point in space, are represented as analytic expressions over the edges of the integration triangle. They can be used to solve integral equations defined on polygonal boundaries via the collocation method or may be utilized as analytic expressions for the inner integrals in the Galerkin technique. In addition, the constant element approximation can be directly obtained with no extra effort. Sample problems solved by the collocation boundary element method for the Laplace equation are included to validate the proposed formulae. Published in 2008 by John Wiley & Sons, Ltd. [source] An incremental formulation for the prediction of two-dimensional fatigue crack growth with curved pathsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2007Ki-Seok Kim Abstract This paper presents a new incremental formulation for predicting the curved growth paths of two-dimensional fatigue cracks. The displacement and traction boundary integral equations (BIEs) are employed to calculate responses of a linear elastic cracked body. The Paris law and the principle of local symmetry are adopted for defining the growth rate and direction of a fatigue crack, respectively. The three governing equations, i.e. the BIEs, the Paris law and the local symmetry condition, are non-linear with respect to the crack growth path and unknowns on the boundary. Iterative forms of three governing equations are derived to solve problems of the fatigue crack growth by the Newton,Raphson method. The incremental crack path is modelled as a parabola defined by the crack-tip position, and the trapezoidal rule is employed to integrate the Paris law. The validity of the proposed method is demonstrated by two numerical examples of plates with an edge crack. Copyright © 2007 John Wiley & Sons, Ltd. [source] Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicatorsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002K. H. Muci-Küchler Abstract In this work, a new global reanalysis technique for the efficient computation of stresses and error indicators in two-dimensional elastostatic problems is presented. In the context of the boundary element method, the global reanalysis technique can be viewed as a post-processing activity that is carried out once an analysis using Lagrangian elements has been performed. To do the reanalysis, the functional representation for the displacements is changed from Lagrangian to Hermite, introducing the nodal values of the tangential derivatives of those quantities as additional degrees of freedom. Next, assuming that the nodal values of the displacements and the tractions remain practically unchanged from the ones obtained in the analysis using Lagrangian elements, the tangent derivative boundary integral equations are collocated at each functional node in order to determine the additional degrees of freedom that were introduced. Under this scheme, a second system of equations is generated and, once it is solved, the nodal values of the tangential derivatives of the displacements are obtained. This approach gives more accurate results for the stresses at the nodes since it avoids the need to differentiate the shape functions in order to obtain the normal strain in the tangential direction. When compared with the use of Hermite elements, the global reanalysis technique has the attraction that the user does not have to give as input data the additional information required by this type of elements. Another important feature of the proposed approach is that an efficient error indicator for the values of the stresses can also be obtained comparing the values for the stresses obtained through the use of Lagrangian elements and the global reanalysis technique. Copyright © 2001 John Wiley & Sons, Ltd. [source] On the spectrum of the electric field integral equation and the convergence of the moment methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2001Karl F. Warnick Abstract Existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self-coupling of surface wave modes, the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations. From the spectrum of the EFIE, the solution error introduced by discretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discretization length for low-order bases with exact integration of matrix elements, and is first order if an approximate quadrature rule is employed. Comparison with numerical results demonstrates the validity of these condition number and solution error estimates. The spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics. Copyright © 2001 John Wiley & Sons, Ltd. [source] Meshless Galerkin analysis of Stokes slip flow with boundary integral equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009Xiaolin Li Abstract This paper presents a novel meshless Galerkin scheme for modeling incompressible slip Stokes flows in 2D. The boundary value problem is reformulated as boundary integral equations of the first kind which is then converted into an equivalent variational problem with constraint. We introduce a Lagrangian multiplier to incorporate the constraint and apply the moving least-squares approximations to generate trial and test functions. In this boundary-type meshless method, boundary conditions can be implemented exactly and system matrices are symmetric. Unlike the domain-type method, this Galerkin scheme requires only a nodal structure on the bounding surface of a body for approximation of boundary unknowns. The convergence and abstract error estimates of this new approach are given. Numerical examples are also presented to show the efficiency of the method. Copyright © 2009 John Wiley & Sons, Ltd. [source] A domain decomposition method for modelling Stokes flow in porous materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002Guangli Liu Abstract An algorithm is presented for solving the Stokes equation in large disordered two-dimensional porous domains. In this work, it is applied to random packings of discs, but the geometry can be essentially arbitrary. The approach includes the subdivision of the domain and a subsequent application of boundary integral equations to the subdomains. This gives a block diagonal matrix with sparse off-block components that arise from shared variables on internal subdomain boundaries. The global problem is solved using a biconjugate gradient routine with preconditioning. Results show that the effectiveness of the preconditioner is strongly affected by the subdomain structure, from which a methodology is proposed for the domain decomposition step. A minimum is observed in the solution time versus subdomain size, which is governed by the time required for preconditioning, the time for vector multiplications in the biconjugate gradient routine, the iterative convergence rate and issues related to memory allocation. The method is demonstrated on various domains including a random 1000-particle domain. The solution can be used for efficient recovery of point velocities, which is discussed in the context of stochastic modelling of solute transport. Copyright © 2002 John Wiley & Sons, Ltd. [source] Boundary integral equations for two-dimensional low Reynolds number flow past a porous bodyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2009Mirela Kohr Abstract In this paper we use the method of matched asymptotic expansions in order to study the two-dimensional steady flow of a viscous incompressible fluid at low Reynolds number past a porous body of arbitrary shape. One assumes that the flow inside the porous body is described by the Brinkman model, i.e. by the continuity and Brinkman equations, and that the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. By considering some indirect boundary integral representations, the inner problems are reduced to uniquely solvable systems of Fredholm integral equations of the second kind in some Sobolev or Hölder spaces, while the outer problems are solved by using the singularity method. It is shown that the force exerted by the exterior flow on the porous body admits an asymptotic expansion with respect to low Reynolds number, whose terms depend on the solutions of the abovementioned system of boundary integral equations. In addition, the case of small permeability of the porous body is also treated. Copyright © 2008 John Wiley & Sons, Ltd. [source] Weak solutions for time-dependent boundary integral equations associated with the bending of elastic plates under combined boundary dataMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2004Igor Chudinovich Abstract The existence, uniqueness, stability, and integral representation of distributional solutions are investigated for the equations of motion of a thin elastic plate with a combination of displacement and moment-stress components prescribed on the boundary. Copyright © 2004 John Wiley & Sons, Ltd. [source] On a quadrature algorithm for the piecewise linear wavelet collocation applied to boundary integral equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2003Andreas Rathsfeld Abstract In this paper, we consider a piecewise linear collocation method for the solution of a pseudo-differential equation of order r=0, ,1 over a closed and smooth boundary manifold. The trial space is the space of all continuous and piecewise linear functions defined over a uniform triangular grid and the collocation points are the grid points. For the wavelet basis in the trial space we choose the three-point hierarchical basis together with a slight modification near the boundary points of the global patches of parametrization. We choose linear combinations of Dirac delta functionals as wavelet basis in the space of test functionals. For the corresponding wavelet algorithm, we show that the parametrization can be approximated by low-order piecewise polynomial interpolation and that the integrals in the stiffness matrix can be computed by quadrature, where the quadrature rules are composite rules of simple low-order quadratures. The whole algorithm for the assembling of the matrix requires no more than O(N [logN]3) arithmetic operations, and the error of the collocation approximation, including the compression, the approximative parametrization, and the quadratures, is less than O(N,(2,r)/2). Note that, in contrast to well-known algorithms by Petersdorff, Schwab, and Schneider, only a finite degree of smoothness is required. In contrast to an algorithm of Ehrich and Rathsfeld, no multiplicative splitting of the kernel function is required. Beside the usual mapping properties of the integral operator in low order Sobolev spaces, estimates of Calderón,Zygmund type are the only assumptions on the kernel function. 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