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Numerical Experiments (numerical + experiment)
Kinds of Numerical Experiments Selected AbstractsCompressing infrared spectrum of exhaust plume by waveletsHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 2 2010Yanming Wang Abstract A study on multivariate calibration for the infrared spectrum of rocket exhaust plume was presented. As samples taken in the data set, the apparent infrared radiative properties of the high-temperature plume flowfield consisted of variable concentrations gas components and were obtained by using a flux method combined with a narrow-band model and Mie theory. The discrete wavelet transformation as a pre-processing tool was carried out to decompose the infrared spectrum and compress the data set. The compressed data regression model was applied to simultaneous multi-component concentrations for determination of the exhaust plume. The compression performance with several wavelet functions at different resolution scales was studied, and the prediction reliability of the compressed regression model was investigated. Numerical experiment results show that the wavelet transform performs an effective compression preprocessing technique in multivariate calibration and enhances the ability in characteristic extraction of the exhaust plume infrared spectrum. Using the compressed data regression model, the reconstructing results are almost identical when compared to the original spectrum, and the original size of the data set has been reduced to about 5% while the computational time needed decreases significantly. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20280 [source] Meltwater discharge through the subglacial bed and its land-forming consequences from numerical experiments in the Polish lowland during the last glaciationEARTH SURFACE PROCESSES AND LANDFORMS, Issue 4 2009Jan A. Piotrowski Abstract Numerical experiments suggest that the last glaciation severely affected the upper lithosphere groundwater system in NW Poland: primarily its flow pattern, velocities and fluxes. We have simulated subglacial groundwater flow in two and three spatial dimensions using finite difference codes for steady-state and transient conditions. The results show how profoundly the ice sheet modifies groundwater pressure heads beneath and some distance beyond the ice margin. All model runs show water discharge at the ice forefield driven by ice-sheet-thickness-modulated, down-ice-decreasing hydraulic heads. In relation to non-glacial times, the transient 3D model shows significant changes in the groundwater flow directions in a regionally extensive aquifer ca. 90 m below the ice,bed interface and up to 40 km in front of the glacier. Comparison with empirical data suggests that, depending on the model run, only between 5 and 24% of the meltwater formed at the ice sole drained through the bed as groundwater. This is consistent with field observations documenting abundant occurrence of tunnel valleys, indicating that the remaining portion of basal meltwater was evacuated through a channelized subglacial drainage system. Groundwater flow simulation suggests that in areas of very low hydraulic conductivity and adverse subglacial slopes water ponding at the ice sole was likely. In these areas the relief shows distinct palaeo-ice lobes, indicating fast ice flow, possibly triggered by the undrained water at the ice,bed interface. Owing to the abundance of low-permeability strata in the bed, the simulated groundwater flow depth is less than ca. 200 m. Copyright © 2009 John Wiley & Sons, Ltd. [source] Prediction of sea surface temperature from the global historical climatology network dataENVIRONMETRICS, Issue 3 2004Samuel S. P. Shen Abstract This article describes a spatial prediction method that predicts the monthly sea surface temperature (SST) anomaly field from the land only data. The land data are from the Global Historical Climatology Network (GHCN). The prediction period is 1880,1999 and the prediction ocean domain extends from 60°S to 60°N with a spatial resolution 5°×5°. The prediction method is a regression over the basis of empirical orthogonal functions (EOFs). The EOFs are computed from the following data sets: (a) the Climate Prediction Center's optimally interpolated sea surface temperature (OI/SST) data (1982,1999); (b) the National Climatic Data Center's blended product of land-surface air temperature (1992,1999) produced from combining the Special Satellite Microwave Imager and GHCN; and (c) the National Centers for Environmental Prediction/National Center for Atmospheric Research Reanalysis data (1982,1999). The optimal prediction method minimizes the first- M -mode mean square error between the true and predicted anomalies over both land and ocean. In the optimization process, the data errors of the GHCN boxes are used, and their contribution to the prediction error is taken into account. The area-averaged root mean square error of prediction is calculated. Numerical experiments demonstrate that this EOF prediction method can accurately recover the global SST anomalies during some circulation patterns and add value to the SST bias correction in the early history of SST observations and the validation of general circulation models. Our results show that (i) the land only data can accurately predict the SST anomaly in the El Nino months when the temperature anomaly structure has very large correlation scales, and (ii) the predictions for La Nina, neutral, or transient months require more EOF modes because of the presence of the small scale structures in the anomaly field. Copyright © 2004 John Wiley & Sons, Ltd. [source] Three-dimensional trajectories of 60Co-labelled earthworms in artificial cores of soilEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 3 2001Y. Capowiez Summary Information on earthworm burrowing behaviour is scarce and therefore the evolution of the macroporosity related to earthworm activities is still poorly known. We have designed a new apparatus, ,Colonne Gamma', to follow the three-dimensional trajectories of radio-labelled earthworms in artificial cores of soil. Earthworms are radio-labelled by injecting into their coelomic cavity a small source of 60Co (volume 0.1 mm3, intensity 13.5 ,Ci). The emission of gamma rays is recorded by three detectors carried by a disc that oscillates vertically around the soil core where the earthworm is introduced. We have also developed a deterministic model to estimate the positions of the 60Co source from the number of gamma rays received by each detector during an oscillation. Numerical experiments showed that the uncertainties of estimates were less than 3 mm for each coordinate. To validate the results, we tracked the trajectory (one position every 4 minutes) of a radio-labelled earthworm for 1 week and compared it with the skeleton of the macroporosity obtained by computer assisted tomography of the same soil core. There was a general qualitative agreement between the trajectory and the skeleton. Moreover, based on the precise study of the successive positions of the earthworm we could distinguish two different kinds of activities in the trajectory: displacement and digging events. The ,Colonne Gamma' apparatus therefore has great potential for studies of the ecology and the behaviour of earthworms. [source] Inter-cell coordination in wireless data networksEUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS, Issue 3 2006Thomas Bonald Over the past few years, the design and performance of channel-aware scheduling strategies have attracted huge interest. In the present paper, we examine a somewhat different notion of scheduling, namely coordination of transmissions among base stations, which has received little attention so far. The inter-cell coordination comprises two key elements: (i) interference avoidance and (ii) load balancing. The interference avoidance involves coordinating the activity phases of interfering base stations so as to increase transmission rates. The load balancing aims at diverting traffic from heavily loaded cells to lightly loaded cells. Numerical experiments demonstrate that inter-cell scheduling may provide significant capacity gains. Copyright © 2006 AEIT [source] Full waveform inversion of seismic waves reflected in a stratified porous mediumGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2010Louis De Barros SUMMARY In reservoir geophysics applications, seismic imaging techniques are expected to provide as much information as possible on fluid-filled reservoir rocks. Since seismograms are, to some degree, sensitive to the mechanical parameters and fluid properties of porous media, inversion methods can be devised to directly estimate these quantities from the waveforms obtained in seismic reflection experiments. An inversion algorithm that uses a generalized least-squares, quasi-Newton approach is described to determine the porosity, permeability, interstitial fluid properties and mechanical parameters of porous media. The proposed algorithm proceeds by iteratively minimizing a misfit function between observed data and synthetic wavefields computed with the Biot theory. Simple models consisting of plane-layered, fluid-saturated and poro-elastic media are considered to demonstrate the concept and evaluate the performance of such a full waveform inversion scheme. Numerical experiments show that, when applied to synthetic data, the inversion procedure can accurately reconstruct the vertical distribution of a single model parameter, if all other parameters are perfectly known. However, the coupling between some of the model parameters does not permit the reconstruction of several model parameters at the same time. To get around this problem, we consider composite parameters defined from the original model properties and from a priori information, such as the fluid saturation rate or the lithology, to reduce the number of unknowns. Another possibility is to apply this inversion algorithm to time-lapse surveys carried out for fluid substitution problems, such as CO2 injection, since in this case only a few parameters may vary as a function of time. We define a two-step differential inversion approach which allows us to reconstruct the fluid saturation rate in reservoir layers, even though the medium properties are poorly known. [source] A quantitative identification technique for a two-dimensional subsurface defect based on surface temperature measurementHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2009Chunli Fan Abstract The inverse identification of a subsurface defect boundary is an important part of an inverse heat conduction problem, and is also the basis for the quantitative development of a nondestructive thermographic inspection technique. For the commonly encountered quantitative thermographic defect identification problem when the test piece is heated from one part of the outer boundary, our previous study showed that some parts of the defect boundary are sensitive to the initial defect boundary prediction of the conjugate gradient method. In this paper, the heat transfer mechanism inside a test piece with this problem is analyzed by building a two-dimensional model. A new method, the multiple measurements combination method (MMCM), is also presented which combines the identification algorithm study with the optimization of the thermographic detection technique to solve the problem. Numerical experiments certified the effectiveness of the present method. The temperature measurement error and the initial prediction of the defect boundary shape have little effect on the identification result. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20251 [source] Particle Swarm Optimization with Diverse ParametersIEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 4 2008Mari Takei Student Member Abstract This paper proposes a particle swarm optimization (PSO) with diverse parameters that achieve an appropriate balance between diversification and intensification during the search based on numerical stability analysis. Numerical experiments using seven typical benchmark problems with 100, 500, and 1000 dimensions validate the robustness and search capabilities of the proposed PSO. © 2008 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source] Numerical analysis of the rectangular domain decomposition methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2009Younbae Jun Abstract When solving parabolic partial differential equations using finite difference non-overlapping domain decomposition methods, one often uses the stripwise decomposition of spatial domain and it can be extended to the rectangular decomposition without further analysis. In this paper, we analyze the rectangular decomposition when the modified implicit prediction (MIP) algorithm is used. We show that the performance of the rectangular decomposition and the stripwise decomposition is different. We compare spectral radius, maximum error, efficiency, and total operations of the rectangular and the stripwise decompositions. We investigate the accuracy of the interface of the rectangular decomposition and the effects of the correction phase of the rectangular decomposition. Numerical experiments have been done in both two and three spatial dimensions and show that the rectangular decomposition is not better than the stripwise decomposition. Copyright © 2008 John Wiley & Sons, Ltd. [source] A stopping criterion for the conjugate gradient algorithm in the framework of anisotropic adaptive finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2009M. Picasso Abstract We propose a simple stopping criterion for the conjugate gradient (CG) algorithm in the framework of anisotropic, adaptive finite elements for elliptic problems. The goal of the adaptive algorithm is to find a triangulation such that the estimated relative error is close to a given tolerance TOL. We propose to stop the CG algorithm whenever the residual vector has Euclidian norm less than a small fraction of the estimated error. This stopping criterion is based on a posteriori error estimates between the true solution u and the computed solution u (the superscript n stands for the CG iteration number, the subscript h for the typical mesh size) and on heuristics to relate the error between uh and u to the residual vector. Numerical experiments with anisotropic adaptive meshes show that the total number of CG iterations can be divided by 10 without significant discrepancy in the computed results. Copyright © 2008 John Wiley & Sons, Ltd. [source] Energy-adjustable mechanism of the combined hybrid finite element method and improvement of Zienkiewicz's plate-elementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2005Xiao-ping Xie Abstract The combined hybrid finite element method for plate bending problems allows arbitrary combinations of deflection interpolation and bending moment approximations. A novel expression of the approach discloses the energy-adjustable mechanism of the hybrid variational principle to enhance accuracy and stability of displacement-based finite element models. For a given displacement approximation, appropriate choices of the bending moment mode and the combination parameter , , (0,1) can lead to accurate energy approximation which generally yields numerically high accuracy of the displacement and bending moment approximations. By virtue of this mechanism, improvement of Zienkiewicz's triangular plate-element is discussed. The deflection is approximated by Zienkiewicz incomplete cubic interpolation. And three kinds of bending moments approximations are considered: a 3-parameter constant mode, a 5-parameter incomplete linear mode, and a 9-parameter linear mode. Since the parameters of the assumed bending moments modes can be eliminated at an element level, the computational cost of the combined hybrid counterparts of Zienkiewicz's triangle are as same as that of Zienkiewicz's triangle. Numerical experiments show that the combined hybrid versions can attain high accuracy at coarse meshes. Copyright © 2005 John Wiley & Sons, Ltd. [source] Multilevel hybrid spectral element ordering algorithmsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2005Jennifer A. Scott Abstract For frontal solvers to perform well on finite-element problems it is essential that the elements are ordered for a small wavefront. Multilevel element ordering algorithms have their origins in the profile reduction algorithm of Sloan but for large problems often give significantly smaller wavefronts. We examine a number of multilevel variants with the aim of finding the best methods to include within a new state-of-the-art frontal solver for finite-element applications that we are currently developing. Numerical experiments are performed using a range of problems arising from real applications and comparisons are made with existing element ordering algorithms. Copyright © 2005 John Wiley & Sons, Ltd. [source] Algebraic preconditioning versus direct solvers for dense linear systems as arising in crack propagation problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2005Erik Bängtsson Abstract Preconditioned iterative solution methods are compared with the direct Gaussian elimination method to solve dense linear systems Ax=b which originate from problems, discretized by boundary element method (BEM) techniques. Numerical experiments are presented and compared with the direct solution method available in a commercial BEM package, which show that the preconditioned iterative schemes are highly competitive with respect to both arithmetic operations required and memory demands. Copyright © 2004 John Wiley & Sons, Ltd. [source] Application of the additive Schwarz method to large scale Poisson problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2004K. M. Singh Abstract This paper presents an application of the additive Schwarz method to large scale Poisson problems on parallel computers. Domain decomposition in rectangular blocks with matching grids on a structured rectangular mesh has been used together with a stepwise approximation to approximate sloping sides and complicated geometric features. A seven-point stencil based on central difference scheme has been used for the discretization of the Laplacian for both interior and boundary grid points, and this results in a symmetric linear algebraic system for any type of boundary conditions. The preconditioned conjugate gradient method has been used as an accelerator for the additive Schwarz method, and three different methods have been assessed for the solution of subdomain problems. Numerical experiments have been performed to determine the most suitable set of subdomain solvers and the optimal accuracy of subdomain solutions; to assess the effect of different decompositions of the problem domain; and to evaluate the parallel performance of the additive Schwarz preconditioner. Application to a practical problem involving complicated geometry is presented which establishes the efficiency and robustness of the method. Copyright © 2004 John Wiley & Sons, Ltd. [source] A preconditioner freeze strategy for numerical solution of compressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2003R. S. Silva Abstract It is well known that Krylov,Schwarz methods are well suited for solving linear systems of equations in high-latency, distributed memory environments and constitute powerful tools when combined with Newton,Krylov methods to solve Computational Fluid Dynamics problems. Nevertheless, the computational costs related to the Jacobian and the preconditioner evaluation can sometimes be prohibitive. In this work a strategy to reduce these costs is presented, based on evaluating a new preconditioner only after it had been frozen for several time steps. Numerical experiments show the computational gain achieved with the proposed strategy. Copyright © 2003 John Wiley & Sons, Ltd. [source] Computation of a few smallest eigenvalues of elliptic operators using fast elliptic solversINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2001Janne Martikainen Abstract The computation of a few smallest eigenvalues of generalized algebraic eigenvalue problems is studied. The considered problems are obtained by discretizing self-adjoint second-order elliptic partial differential eigenvalue problems in two- or three-dimensional domains. The standard Lanczos algorithm with the complete orthogonalization is used to compute some eigenvalues of the inverted eigenvalue problem. Under suitable assumptions, the number of Lanczos iterations is shown to be independent of the problem size. The arising linear problems are solved using some standard fast elliptic solver. Numerical experiments demonstrate that the inverted problem is much easier to solve with the Lanczos algorithm that the original problem. In these experiments, the underlying Poisson and elasticity problems are solved using a standard multigrid method. Copyright © 2001 John Wiley & Sons, Ltd. [source] A Cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Phong B. H. Le Abstract In this paper, high-order systems are reformulated as first-order systems, which are then numerically solved by a collocation method. The collocation method is based on Cartesian discretization with 1D-integrated radial basis function networks (1D-IRBFN) (Numer. Meth. Partial Differential Equations 2007; 23:1192,1210). The present method is enhanced by a new boundary interpolation technique based on 1D-IRBFN, which is introduced to obtain variable approximation at irregular points in irregular domains. The proposed method is well suited to problems with mixed boundary conditions on both regular and irregular domains. The main results obtained are (a) the boundary conditions for the reformulated problem are of Dirichlet type only; (b) the integrated RBFN approximation avoids the well-known reduction of convergence rate associated with differential formulations; (c) the primary variable (e.g. displacement, temperature) and the dual variable (e.g. stress, temperature gradient) have similar convergence order; (d) the volumetric locking effects associated with incompressible materials in solid mechanics are alleviated. Numerical experiments show that the proposed method achieves very good accuracy and high convergence rates. Copyright © 2009 John Wiley & Sons, Ltd. [source] A hybridizable discontinuous Galerkin method for linear elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2009S.-C. Soon Abstract This paper describes the application of the so-called hybridizable discontinuous Galerkin (HDG) method to linear elasticity problems. The method has three significant features. The first is that the only globally coupled degrees of freedom are those of an approximation of the displacement defined solely on the faces of the elements. The corresponding stiffness matrix is symmetric, positive definite, and possesses a block-wise sparse structure that allows for a very efficient implementation of the method. The second feature is that, when polynomials of degree k are used to approximate the displacement and the stress, both variables converge with the optimal order of k+1 for any k,0. The third feature is that, by using an element-by-element post-processing, a new approximate displacement can be obtained that converges at the order of k+2, whenever k,2. Numerical experiments are provided to compare the performance of the HDG method with that of the continuous Galerkin (CG) method for problems with smooth solutions, and to assess its performance in situations where the CG method is not adequate, that is, when the material is nearly incompressible and when there is a crack. Copyright © 2009 John Wiley & Sons, Ltd. [source] Dispersion analysis of the meshfree radial point interpolation method for the Helmholtz equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009Christina Wenterodt Abstract When numerical methods such as the finite element method (FEM) are used to solve the Helmholtz equation, the solutions suffer from the so-called pollution effect which leads to inaccurate results, especially for high wave numbers. The main reason for this is that the wave number of the numerical solution disagrees with the wave number of the exact solution, which is known as dispersion. In order to obtain admissible results a very high element resolution is necessary and increased computational time and memory capacity are the consequences. In this paper a meshfree method, namely the radial point interpolation method (RPIM), is investigated with respect to the pollution effect in the 2D-case. It is shown that this methodology is able to reduce the dispersion significantly. Two modifications of the RPIM, namely one with polynomial reproduction and another one with a problem-dependent sine/cosine basis, are also described and tested. Numerical experiments are carried out to demonstrate the advantages of the method compared with the FEM. For identical discretizations, the RPIM yields considerably better results than the FEM. Copyright © 2008 John Wiley & Sons, Ltd. [source] On the computation of steady-state compressible flows using a discontinuous Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008Hong Luo Abstract Computation of compressible steady-state flows using a high-order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics-based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low-storage p -multigrid method is used for solving the governing compressible Euler equations to obtain steady-state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady-state flows. Copyright © 2007 John Wiley & Sons, Ltd. [source] FETI-DP, BDDC, and block Cholesky methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2006Jing Li Abstract The FETI-DP and BDDC algorithms are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal continuity constraints in these algorithms, a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom. With the new formulation of these algorithms, a simplified proof is provided that the spectra of a pair of FETI-DP and BDDC algorithms, with the same set of primal constraints, are essentially the same. Numerical experiments for a two-dimensional Laplace's equation also confirm this result. Copyright © 2005 John Wiley & Sons, Ltd. [source] Smart element method II.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005An element based on the finite Eshelby tensor Abstract In this study, we apply the newly derived finite Eshelby tensor in a variational multiscale formulation to construct a smart element through a more accurate homogenization procedure. The so-called Neumann,Eshelby tensor for an inclusion in a finite domain is used in the fine scale feedback procedure to take into account the interactions among different scales and elements. Numerical experiments have been conducted to compare the performance and robustness of the new element to earlier formulations. The results showed that the smart element constructed via the Neumann,Eshelby tensor of a finite domain provides better numerical accuracy than that constructed via the Eshelby tensor of an infinite domain. Moreover, it can relieve volumetric locking. Copyright © 2005 John Wiley & Sons, Ltd. [source] A freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Jie Shen Abstract In this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Cox,de Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and does not require CAD information; (3) freeform shape optimization of arbitrary polygonal or polyhedral meshes. Numerical experiments indicate the effectiveness of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd. [source] From mixed finite elements to finite volumes for elliptic PDEs in two and three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Anis Younes Abstract The link between Mixed Finite Element (MFE) and Finite Volume (FV) methods applied to elliptic partial differential equations has been investigated by many authors. Recently, a FV formulation of the mixed approach has been developed. This approach was restricted to 2D problems with a scalar for the parameter used to calculate fluxes from the state variable gradient. This new approach is extended to 2D problems with a full parameter tensor and to 3D problems. The objective of this new formulation is to reduce the total number of unknowns while keeping the same accuracy. This is achieved by defining one new variable per element. For the 2D case with full parameter tensor, this new formulation exists for any kind of triangulation. It allows the reduction of the number of unknowns to the number of elements instead of the number of edges. No additional assumptions are required concerning the averaging of the parameter in hetero- geneous domains. For 3D problems, we demonstrate that the new formulation cannot exist for a general 3D tetrahedral discretization, unlike in the 2D problem. However, it does exist when the tetrahedrons are regular, or deduced from rectangular parallelepipeds, and allows reduction of the number of unknowns. Numerical experiments and comparisons between both formulations in 2D show the efficiency of the new formulation. Copyright © 2003 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 general high-order finite element formulation for shells at large strains and finite rotationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Y. Ba Abstract For hyperelastic shells with finite rotations and large strains a p -finite element formulation is presented accommodating general kinematic assumptions, interpolation polynomials and particularly general three-dimensional hyperelastic constitutive laws. This goal is achieved by hierarchical, high-order shell models. The tangent stiffness matrices for the hierarchical shell models are derived by computer algebra. Both non-hierarchical, nodal as well as hierarchical element shape functions are admissible. Numerical experiments show the high-order formulation to be less prone to locking effects. Copyright © 2003 John Wiley & Sons, Ltd. [source] A reproducing kernel method with nodal interpolation propertyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2003Jiun-Shyan Chen Abstract A general formulation for developing reproducing kernel (RK) interpolation is presented. This is based on the coupling of a primitive function and an enrichment function. The primitive function introduces discrete Kronecker delta properties, while the enrichment function constitutes reproducing conditions. A necessary condition for obtaining a RK interpolation function is an orthogonality condition between the vector of enrichment functions and the vector of shifted monomial functions at the discrete points. A normalized kernel function with relative small support is employed as the primitive function. This approach does not employ a finite element shape function and therefore the interpolation function can be arbitrarily smooth. To maintain the convergence properties of the original RK approximation, a mixed interpolation is introduced. A rigorous error analysis is provided for the proposed method. Optimal order error estimates are shown for the meshfree interpolation in any Sobolev norms. Optimal order convergence is maintained when the proposed method is employed to solve one-dimensional boundary value problems. Numerical experiments are done demonstrating the theoretical error estimates. The performance of the method is illustrated in several sample problems. Copyright © 2003 John Wiley & Sons, Ltd. [source] Stabilized finite element method for viscoplastic flow: formulation with state variable evolutionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Antoinette M. Maniatty Abstract A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady-state metal-forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well-known instabilities, one due to the incompressibility constraint and one due to the convection-type state variable equation. Both of these instabilities are handled by adding mesh-dependent stabilization terms, which are functions of the Euler,Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton,Raphson implementation into an object-oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non-linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal-forming problems show that the stabilized finite element method is effective and efficient for non-linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd. [source] On the optimal cooling strategy for variable-speed continuous castingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002D. Constales Abstract In this paper, we consider the inverse problem of determining the optimal cooling parameters for continuous casting under changing casting speed. We rely on automatic differentiation to support different search methods for the parameter values that will minimize a given cost functional, which can include a variety of criteria: surface temperature evolution and variation, interface position, full solidification point. In the direct problem we use a fixed-domain transformation to solve the corresponding free-boundary problem to high accuracy. Numerical experiments are provided to illustrate and support the effectiveness of the present concept. Copyright © 2001 John Wiley & Sons, Ltd. [source] An accurate gradient and Hessian reconstruction method for cell-centered finite volume discretizations on general unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010Lee J. Betchen Abstract In this paper, a novel reconstruction of the gradient and Hessian tensors on an arbitrary unstructured grid, developed for implementation in a cell-centered finite volume framework, is presented. The reconstruction, based on the application of Gauss' theorem, provides a fully second-order accurate estimate of the gradient, along with a first-order estimate of the Hessian tensor. The reconstruction is implemented through the construction of coefficient matrices for the gradient components and independent components of the Hessian tensor, resulting in a linear system for the gradient and Hessian fields, which may be solved to an arbitrary precision by employing one of the many methods available for the efficient inversion of large sparse matrices. Numerical experiments are conducted to demonstrate the accuracy, robustness, and computational efficiency of the reconstruction by comparison with other common methods. Copyright © 2009 John Wiley & Sons, Ltd. 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