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Fundamental Solutions (fundamental + solution)
Selected AbstractsSemi-analytical far field model for three-dimensional finite-element analysisINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2004James P. Doherty Abstract A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non-linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three-dimensional finite-elements with the recently developed scaled boundary finite-element method. The scaled boundary finite-element method is a semi-analytical technique based on finite-elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co-ordinate direction, but, unlike the boundary-element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three-dimensional finite-element domain with the stiffness matrix of the unbounded scaled boundary finite-element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co-ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd. [source] An efficient time-domain damping solvent extraction algorithm and its application to arch dam,foundation interaction analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2008Hong Zhong Abstract The dynamic structure,unbounded foundation interaction plays an important role in the seismic response of structures. The damping solvent extraction (DSE) method put forward by Wolf and Song has a great advantage of simplicity, with no singular integrals to be evaluated, no fundamental solution required and convolution integrals avoided. However, implementation of DSE in the time domain to large-scale engineering problems is associated with enormous difficulties in evaluating interaction forces on the structure,unbounded foundation interface, because the displacement on the corresponding interface is an unknown vector to be found. Three sets of interrelated large algebraic equations have to be solved simultaneously. To overcome these difficulties, an efficient algorithm is presented, such that the solution procedure can be greatly simplified and computational effort considerably saved. To verify its accuracy, two examples with analytical solutions were investigated, each with a parameter analysis on the domain size and amount of artificial damping. Then with the parameters suggested in the parameter study, the complex frequency,response functions and earthquake time history analysis of Morrow Point dam were presented to demonstrate the applicability and efficiency of DSE approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] The boundary element method for solving the Laplace equation in two-dimensions with oblique derivative boundary conditionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2007D. Lesnic Abstract In this communication, we extend the Neumann boundary conditions by adding a component containing the tangential derivative, hence producing oblique derivative boundary conditions. A variant of Green's formula is employed to translate the tangential derivative to the fundamental solution in the boundary element method (BEM). The two-dimensional steady-state heat conduction with the imposed oblique boundary condition has been tested in smooth, piecewise smooth and multiply connected domains in which the Laplace equation is the governing equation, producing results at the boundary in excellent agreement with the available analytical solutions. Convergence of the normal and tangential derivatives at the boundary is also achieved. The numerical boundary data are then used to successfully calculate the values of the solution at interior points again. The outlined test cases have been repeated with various boundary element meshes, indicating that the accuracy of the numerical results increases with increasing boundary discretization. Copyright © 2006 John Wiley & Sons, Ltd. [source] Time 2D fundamental solution for saturated porous media with incompressible fluidINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2005Behrouz Gatmiri Abstract The derivation of analytical transient two-dimensional fundamental solution for porous media saturated with incompressible fluid in u-p formulation is discussed in detail. First, the explicit Laplace transform solution in terms of solid displacements and fluid pressure are obtained. Then, the closed-form time-dependent fundamental solution is derived by the analytical inversion of the Laplace transform solution. Finally, a set of numerical results is presented to investigate the accuracy of the proposed solution. It is shown that this solution can be considered as a good approximation of exact solution, especially for the long time. Copyright © 2004 John Wiley & Sons, Ltd. [source] Boundary solution of Poisson's equation using radial basis function collocated on Gaussian quadrature nodesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2001M. Elansari Abstract In the solution of Poisson's equation using either the dual reciprocity boundary element method or the method of fundamental solution, radial basis functions (RBFs) are used to approximate the right-hand side of the governing partial differential equation to eliminate the domain integration. This paper shows that if the RBF interpolation is collocated on the Gaussian quadrature nodes, we seem to observe superconvergence behaviour. This behaviour is demonstrated using a series of numerical examples. Copyright © 2001 John Wiley & Sons, Ltd. [source] Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedraINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003Seppo Järvenpää Abstract A numerical solution of integral equations typically requires calculation of integrals with singular kernels. The integration of singular terms can be considered either by purely numerical techniques, e.g. Duffy's method, polar co-ordinate transformation, or by singularity extraction. In the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically. This method has been well established for linear and constant shape functions. In this paper we extend the method for polynomial shape functions of arbitrary order. We present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the Helmholtz equation, or its gradient, and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra. The presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high-order basis functions. Numerical experiments show that the developed method leads to a more accurate and robust integration scheme, and in many cases also a faster method than, for example, Duffy's transformation. Copyright © 2003 John Wiley & Sons, Ltd. [source] A hybrid boundary node methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002Jianming Zhang Abstract A new variational formulation for boundary node method (BNM) using a hybrid displacement functional is presented here. The formulation is expressed in terms of domain and boundary variables, and the domain variables are interpolated by classical fundamental solution; while the boundary variables are interpolated by moving least squares (MLS). The main idea is to retain the dimensionality advantages of the BNM, and get a truly meshless method, which does not require a ,boundary element mesh', either for the purpose of interpolation of the solution variables, or for the integration of the ,energy'. All integrals can be easily evaluated over regular shaped domains (in general, semi-sphere in the 3-D problem) and their boundaries. Numerical examples presented in this paper for the solution of Laplace's equation in 2-D show that high rates of convergence with mesh refinement are achievable, and the computational results for unknown variables are most accurate. No further integrations are required to compute the unknown variables inside the domain as in the conventional BEM and BNM. Copyright © 2001 John Wiley & Sons, Ltd. [source] Time-domain BEM solution of convection,diffusion-type MHD equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008N. Bozkaya Abstract The two-dimensional convection,diffusion-type equations are solved by using the boundary element method (BEM) based on the time-dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady-state iteratively. Thus, it is possible to use quite large time increments and stability problems are not encountered. The time-domain BEM solution procedure is tested on some convection,diffusion problems and the MHD duct flow problem with insulated walls to establish the validity of the approach. The numerical results for these sample problems compare very well to analytical results. Then, the BEM formulation of the MHD duct flow problem with arbitrary wall conductivity is obtained for the first time in such a way that the equations are solved together with the coupled boundary conditions. The use of time-dependent fundamental solution enables us to obtain numerical solutions for this problem for the Hartmann number values up to 300 and for several values of conductivity parameter. Copyright © 2007 John Wiley & Sons, Ltd. [source] On finite difference potentials and their applications in a discrete function theoryMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16-18 2002K. Gürlebeck Abstract We present a potential theoretical method which is based on the approximation of the boundary value problem by a finite difference problem on a uniform lattice. At first the discrete fundamental solution of the Laplace equation is studied and the theory of difference potentials is described. In the second part we define a discrete Cauchy integral operator and a Teodorescu transform. In addition a Borel,Pompeiu formula can be formulated. Copyright © 2002 John Wiley & Sons, Ltd. [source] Null-field approach for Laplace problems with circular boundaries using degenerate kernelsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2009Jeng-Tzong Chen Abstract In this article, a semi-analytical method for solving the Laplace problems with circular boundaries using the null-field integral equation is proposed. The main gain of using the degenerate kernels is to avoid calculating the principal values. To fully utilize the geometry of circular boundary, degenerate kernels for the fundamental solution and Fourier series for boundary densities are incorporated into the null-field integral equation. An adaptive observer system is considered to fully employ the property of degenerate kernels in the polar coordinates. A linear algebraic system is obtained without boundary discretization. By matching the boundary condition, the unknown coefficients can be determined. The present method can be seen as one kind of semianalytical approaches since error only attributes to the truncated Fourier series. For the eccentric case, vector decomposition technique for the normal and tangential directions is carefully considered in implementing the hypersingular equation in mathematical essence although we transform it to summability to divergent series. The five advantages, well-posed linear algebraic system, principal value free, elimination of boundary-layer effect, exponential convergence, and mesh free, are achieved. Several examples involving infinite, half-plane, and bounded domains with circular boundaries are given to demonstrate the validity of the proposed method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Green element method for 2D Helmholtz and convection diffusion problems with variable velocity coefficientsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2005Okey Oseloka Onyejekwe Abstract Computation of 2D Helmholtz and transient convection diffusion problems with linear reaction and variable velocity components are implemented with the Green element method (GEM). GEM's fundamental solution which is derived from the diffusion differential operator simplifies the numerical procedure considerably, and together with the Green's second identity, an element to element treatment of the inhomogeneous terms is guaranteed. The reported numerical experiments reveal that the method can be relied on to yield faithful results. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 [source] Recovering acoustic reflectivity using Dirichlet-to-Neumann maps and left- and right-operating adjoint propagatorsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2005M. W. P. Dillen SUMMARY Constructing an image of the Earth subsurface from acoustic wave reflections has previously been described as a recursive downward redatuming of sources and receivers. Most of the methods that have been presented involve reflectivity and propagators associated with one-way wavefield components. In this paper, we consider the reflectivity relation between two-way wavefield components, each a solution of a Helmholtz equation. To construct forward and inverse propagators, and a reflection operator, the invariant-embedding technique is followed, using Dirichlet-to-Neumann maps. Employing bilinear and sesquilinear forms, the forward- and inverse-scattering problems, respectively, are treated analogously. Through these mathematical constructs, the relationship between a causality radiation condition and symmetry, with respect to a bilinear form, is associated with the requirement of an anticausality radiation condition with respect to a sesquilinear form. Using reciprocity, sources and receivers are redatumed recursively to the reflector, employing left- and right-operating adjoint propagators. The exposition of the proposed method is formal, that is numerical applications are not derived. The key to applications lies in the explicit representation, characterization and approximation of the relevant operators (symbols) and fundamental solutions (path integrals). Existing constructive work which could be applied to the proposed method are referred to in the text. [source] The fundamental solution of poroelastic plate saturated by fluid and its applicationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010P. H. Wen Abstract In this paper, the numerical model of the transverse vibrations of a thin poroelastic plate saturated by a fluid was proposed. Two coupled dynamic equations of equilibrium related to the plate deflection and the equivalent moment were established for an isotropic porous medium with uniform porosity. The fundamental solutions for a porous plate were derived both in the Laplace transform domain and in the time domain. A meshless method was developed and demonstrated in the Laplace transform domain for solving two coupled dynamic equations. Numerical examples demonstrated the accuracy of the method of the fundamental solutions and comparisons were made with analytical solutions. The proposed meshless method was shown to be simple to implement and gave satisfactory results for a poroelastic plate dynamic analysis. Copyright © 2009 John Wiley & Sons, Ltd. [source] Poroelastic model for pile,soil interaction in a half-space porous medium due to seismic wavesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2008Jian-Fei Lu Abstract In this paper, frequency domain dynamic response of a pile embedded in a half-space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half-space and a fictitious pile. The extended porous half-space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1-D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half-space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half-space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile,half-space system. Significant differences between conventional single-phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd. [source] Seismic response of slopes subjected to incident SV wave by an improved boundary element approachINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2007Behrouz Gatmiri Abstract In this paper, an improved boundary element approach for 2D elastodynamics in time-domain is presented. This approach consists in the truncation of time integrations, based on the rapid decrease of the fundamental solutions with time. It is shown that an important reduction of the computation time as well as the storage requirement can be achieved. Moreover, for half-plane problems, the size of boundary element (BE) meshes and the computation time can be significantly reduced. The proposed approach is used to study the seismic response of slopes subjected to incident SV waves. It is found that large amplifications take place on the upper surface close to the slope, while attenuations are produced on the lower surface. The results also show that surface motions become very complex when the incident wavelength is comparable with the size of the slope or when the slope is steep. Copyright © 2006 John Wiley & Sons, Ltd. [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] Collocation methods based on radial basis functions for solving stochastic Poisson problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2007Somchart ChantasiriwanArticle first published online: 19 JUN 200 Abstract Collocation methods based on radial basis functions can be used to provide accurate solutions to deterministic problems. For stochastic problems, accurate solutions may not be desirable if they are too sensitive to random inputs. In this paper, four methods are used to solve stochastic Poisson problems by expressing solutions in terms of source terms and boundary conditions. Comparison among the methods reveals that the method based on fundamental solutions performs better than other methods. Copyright © 2006 John Wiley & Sons, Ltd. [source] Coupling BEM/TBEM and MFS for the simulation of transient conduction heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2010António Tadeu Abstract The coupling between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS) is proposed for the transient analysis of conduction heat transfer in the presence of inclusions, thereby overcoming the limitations posed by each method. The full domain is divided into sub-domains, which are modeled using the BEM/TBEM and the MFS, and the coupling of the sub-domains is achieved by imposing the required boundary conditions. The accuracy of the proposed algorithms, using different combinations of BEM/TBEM and MFS formulations, is checked by comparing the resulting solutions against referenced solutions. The applicability of the proposed methodology is shown by simulating the thermal behavior of a solid ring incorporating a crack or a thin inclusion in its wall. The crack is assumed to have null thickness and does not allow diffusion of energy; hence, the heat fluxes are null along its boundary. The thin inclusion is modeled as filled with thermal insulating material. Copyright © 2010 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] Potential field based geometric modelling using the method of fundamental solutionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006Roman Tankelevich Abstract We propose a new geometric modelling method based on the so-called potential field (PF) modelling technique. The harmonic problem associated with this technique is solved numerically using the method of fundamental solutions (MFS). We investigate the applicability of the proposed approach to parametrically defined curves of varying complexity. Based on the MFS, we also provide definitions of the Boolean operations associated with the geometric modelling. Finally, we give practical applications of the method to computer-aided design and manufacturing problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Boundary elements for half-space problems via fundamental solutions: A three-dimensional analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001J. Liang Abstract An efficient solution technique is proposed for the three-dimensional boundary element modelling of half-space problems. The proposed technique uses alternative fundamental solutions of the half-space (Mindlin's solutions for isotropic case) and full-space (Kelvin's solutions) problems. Three-dimensional infinite boundary elements are frequently employed when the stresses at the internal points are required to be evaluated. In contrast to the published works, the strongly singular line integrals are avoided in the proposed solution technique, while the discretization of infinite elements is independent of the finite boundary elements. This algorithm also leads to a better numerical accuracy while the computational time is reduced. Illustrative numerical examples for typical isotropic and transversely isotropichalf-space problems demonstrate the potential applications of the proposed formulations. Incidentally, the results of the illustrative examples also provide a parametric study for the imperfect contact problem. Copyright © 2001 John Wiley & Sons, Ltd. [source] A 2-D time-domain boundary element method with dampingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2001Feng Jin Abstract A new material damping model which is convenient for use in the time-domain boundary element method (TDBEM) is presented and implemented in a proposed procedure. Since only fundamental solutions for linear elastic material are employed, the procedure has high efficiency and is easy to be integrated into current TDBEM codes. Analytical and numerical results for benchmark problems demonstrate that the accuracy of the proposed method is high. Copyright © 2001 John Wiley & Sons, Ltd. [source] Method of fundamental solutions for partial-slip fibrous filtration flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009Shunliu Zhao Abstract In this study a Stokeslet-based method of fundamental solutions (MFS) for two-dimensional low Reynolds number partial-slip flows has been developed. First, the flow past an infinitely long cylinder is selected as a benchmark. The numerical accuracy is investigated in terms of the location and the number of the Stokeslets. The benchmark study shows that the numerical accuracy increases when the Stokeslets are submerged deeper beneath the cylinder surface, as long as the formed linear system remains numerically solvable. The maximum submergence depth increases with the decrease in the number of Stokeslets. As a result, the numerical accuracy does not deteriorate with the dramatic decrease in the number of Stokeslets. A relatively small number of Stokeslets with a substantial submergence depth is thus chosen for modeling fibrous filtration flows. The developed methodology is further examined by application to Taylor,Couette flows. A good agreement between the numerical and analytical results is observed for no-slip and partial-slip boundary conditions. Next, the flow about a representative set of infinitely long cylindrical fibers confined between two planar walls is considered to represent the fibrous filter flow. The obtained flowfield and pressure drop agree very well with the experimental data for this setup of fibers. The developed MFS with submerged Stokeslets is then applied to partial-slip flows about fibers to investigate the slip effect at fiber,fluid interface on the pressure drop. The numerical results compare qualitatively with the analytical solution available for the limit case of infinite number of fibers. Copyright © 2008 John Wiley & Sons, Ltd. [source] A complete boundary integral formulation for compressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2005Yang ZuoshengArticle first published online: 29 DEC 200 Abstract A complete boundary integral formulation for compressible Navier,Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for wall pressure and wall skin friction of two-dimensional compressible laminar viscous flow around airfoils are in good agreement with field numerical methods. Copyright © 2004 John Wiley & Sons, Ltd. [source] Using the theory of constraints thinking processes to complement system dynamics' causal loop diagrams in developing fundamental solutionsINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2006Victoria J. Mabin Abstract Standard OR/MS methods mainly focus on ,hard' aspects of problems represented by quantitative or mathematical formulations. Organisational settings typically pose challenges in the use of such methods, in that they may be inadequate to capture the ,softer' issues surrounding human behaviours, organisational practices and policies. Over the last 20 years, a number of ,soft OR' tools, methods and methodologies have emerged as a means of addressing such challenges, and in this paper, we selectively examine how such methodologies can complement hard and other soft methods. In particular, we examine the potential contribution of the theory of constraints (TOC) and system dynamics (SD) to multi-methodological intervention. We begin by discussing their philosophical underpinnings in relation to other OR/MS methods, and by exploring how such an understanding can provide a theoretical basis for mixing methodologies and for their complementary use. Then, using a case suitable for classroom discussion, the paper provides insights into how the systemic qualities of selected TOC methods and tools may be harnessed in multi-methodological intervention by identifying the communality and complementarity of TOC and other hard and soft OR/MS approaches to problem solving, in particular, the causal loop diagramming method of SD. [source] Elliptic and parabolic problems in unbounded domainsMATHEMATISCHE NACHRICHTEN, Issue 1 2004Patrick Guidotti Abstract We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi-explicit representation formulas via operator-valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadingsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2010Chia-Cheng Tsai Abstract Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth-order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r , 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz-type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source] Poroelastodynamic Boundary Element Method in Time Domain: Numerical AspectsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Martin Schanz Based on Biot's theory the governing equations for a poroelastic continuum are given as a coupled set of partial differential equations (PDEs) for the unknowns solid displacements and pore pressure. Using the Convolution Quadrature Method (CQM) proposed by Lubich a boundary time stepping procedure is established based only on the fundamental solutions in Laplace domain. To improve the numerical behavior of the CQM-based Boundary Element Method (BEM) dimensionless variables are introduced and different choices studied. This will be performed as a numerical study at the example of a poroelastic column. Summarizing the results, the normalization to time and spatial variable as well as on Young's modulus yields the best numerical behavior. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A Finite Interface Crack Interacting With A Subinterface Crack In Metal/Piezoelectric Ceramic BimaterialPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Wen-Ye Tian The "pseudo-traction-electric-displacement' method was adopted to solve the interaction problem between a finite interface crack and a subinterface crack in metal/piezoelectric bimaterial. After deriving the fundamental solutions for a finite interface crack and a special subinterface crack respectively loaded by the normal and tangential concentrated tractions and the concentrated electric displacement, the present interaction problem was reduced to a system of integral equations, which may be solved numerically. The crack tip mode I stress intensity factor was calculated and detailed comparisons of the results derived under the compound mechanical-electric loading conditions and those derived under the purely mechanical loading condition are performed. [source] | ||||||||||||||||