A modified superconvergent patch recovery method and its. The superconvergence patch recovery technique and data. Inmemory integration of existing software components for. Superconvergent patch recovery of finite element solution and l2. Moslemi h, khoei ar 2009 3d adaptive finite element modeling of nonplanar curved crack growth using the weighted superconvergent patch recovery method. The publication of the original spr technique was followed by several works aimed at improving its quality 3638.
For example, an explicit residual based estimate is very easy to implement but it. Remapping method for transferring data between two meshes using a modified iterative spr approach for parallel resolution. In this technique, a continuous and accurate stress is obtained over the entire domain by the recovery of nodal stresses. Recoverybased error estimator for the discontinuous galerkin. In geoscientific studies, conventional bilinear interpolation has been widely used for remapping between logically rectangular grids on the surface of a sphere. Once elements with large errors have been detected, mesh re. However, from the superconvergence theory 12,14,15, we know that the vertexedgeface interpolations have better superconvergent properties than the common lagrange interpolations. Dual techniques are based on the evaluation of two di erent elds, one compatible in displacements and another equilibrated in. The recent progress in computers has enabled a number of complicated natural phenomena to be accurately simulated. The boundary itself isnt a problem as i know the flux on the boundary. Although, the acoustic problems investigated may not be too interesting for you, it covers the scaling aspects as well as large problems with up to 1e6 degrees of freedom. Threedimensional superconvergent patch recovery method and.
Though the preferred candidates will be zzscheme and ppr. Implementation aspects of a recoverybased error estimator in. This method computes stresses at optimal sampling points where the accuracy of stresses is an order of. Material plugins that implement the init function must now return a bool. Superconvergent patch recovery of gradient field on adaptive meshes. Adaptive refinement based on stress recovery technique. Among various computer simulation techniques, the finite element method fem has been most widely used since the invention of the method in late 1950s in a variety of practical fields, such as mechanical, aerospace, nuclear, chemical and civil engineering. The superconvergent cluster recovery method request pdf. To construct a local patch, we first construct a union of mesh elements around a vertex. Firstly, the recovery process is made for element, not for nodes. May 25, 2010 the superconvergent cluster recovery method the superconvergent cluster recovery method huang, yunqing. The prefinement phase is facilitated through the addition and deletion of general serendipity element edge nodes. Center of excellence in structures and earthquake engineering, department of civil engineering, sharif university of technology, p.
Superconvergent patch recovery technique for the finite. The zienkiewiczzhu error estimate is slightly modified for the hierarchical prefinement, and is then applied to three plane elastostatic problems to demonstrate. In this recovery process, it is assumed that stress at nodal values. A modified perturbed lagrangian formulation for contact. One of the things i want to do is implement a backup process using macrium reflect. Apr 14, 2017 i am doing some os maintenance on friends surface pro 2 currently running win 10 pro x64. Jul 15, 2016 recovery is an individualized process. Objectoriented design and methodologies are used to implement the finite element package. In this paper, a new type of gradient recovery method based on the vertexedgeface interpolation. Superconvergent gradient recovery for virtual element methods. The idea is recovering finite element result with least square fit method analogy.
We discuss our implementation of the zienkiewiczzhu error estimator and of selected gradient recovery techniques averaging and superconvergent patch. Since the superconvergent patch scp recovery method is relativity easy to understand and is accurate for a wide range of problems, it was selected for implementation in the educational programmodel. Recovery based submodeling finite element analysis recent. The gaussian quadrature points, which are generally observed to be the same as the barlow points for lower order elements, have so far been used as the sampling points for the superconvergent patch recovery spr. The stabilizing term is iteratively computed using a smooth stress field. In addition to these, the recoverbased technique has been also extended to mesh based pums and the xfem extended finite element method 15. Pdf mesh adaptivity driven by goaloriented locally.
How to fix unlisted windows in system recovery options problem. Recently, some researchers 6, 7 used a weighted superconvergent patch recovery technique in which the recovered stresses are calculated by using weighting parameters. Using linear virtual element method as an example, we propose a universal recovery procedure to improve the accuracy of gradient approximation for numerical methods using general polygonal meshes. The superconvergent cluster recovery method springerlink. These modifications are 1 use of integration points as sampling points, 2 weighted average procedure and 3 introduction of additional nodes. The superconvergent patch derivative recovery method of zienkiewicz and zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. The superconvergent cluster recovery method, journal of. In this post, i wanted to document a widely used solution which is easy to implement, and which is used in research oriented codebases such as feap. Pdf rotational dependence of the superconvergent patch.
A combination of regular subdivision and longestedge bisection is employed. Summary the superconvergent patch recovery spr with bilinear interpolation functions usually gives good values of recovered stresses in an element patch. Among different recovery techniques, the superconvergent patch recovery spr technique has been shown to possess some very attractive features for practical computations. Recovery partition needs optimization windows 10 forums. We try to uncover the superconvergent property of the virtual element methods by doing some local postprocessing only on the degrees of freedom. Pdf new superconvergent points of the 8node serendipity. Superconvergent patch recovery was later further developed to improve its accuracy by adding an equilibrium constraint to the least. We try to uncover the superconvergent property of virtual element methods by doing some local postprocessing only on the degrees of freedom.
There are different techniques for the first step see 1 above, and the most popular one seems to be the patch method or superconvergent patch recovery. Superconvergent patch recovery of finite element solution. After introduction of a suitable lagrange multiplier discretization the method can be simplified to obtain a modified perturbed lagrangian formulation. Superconvergent patch recovery for plate problems using statically admissible stress resultant fields.
It is also shown that the recovered derivative based on the local l 2 projection is not superconvergent in general. A decade has passed since the first appearance of the superconvergent patch recovery spr method introduced by zienkiewicz and zhu the superconvergence patch recovery and a posteriori error. The technique has been tested for a group of widely used linear. The superconvergent patch recovery spr and adaptive finite element refinement. The points are often referred to as superconvergent points whereby the technique is called superconvergent patch recovery for displacements sprd. The technique recovers solution quantities in an element from element patches surrounding the nodes of the elements. Compared to standard gradient recovery methods such as superconvergent patch recovery spr and polynomial preserving recovery ppr, these gradient recovery methods perform more reliably, i. Objectoriented implementation of padaptive finite element. Using the linear virtual element method as an example, we propose a universal gradient recovery procedure to improve the accuracy of gradient approximation for numerical methods using general polygonal meshes. Error estimation based on superconvergent patch recovery using. It is an extension of the superconvergent patch recovery technique presented by zienkiewicz and zhu.
Superconvergence property zhimin zhang yand ahmed naga z department of mathematics, wayne state university, detroit, mi 48202 abstract this is the rst in a series of papers where a new gradient recovery method is introduced and analyzed. Data transfer in the context of adaptive mesh in finite. Superconvergent patch recovery techniques some further. Pdf superconvergent patch recovery for plate problems. Fixing a computer by the use of system recovery options is one of the greatest ways to fix your windows startup problems. Superconvergent patch recovery spr technique previously used for error es timation in the energy norm. Numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent. Superconvergent patch recovery and a posteriori error. Superconvergence behavior matches well with the use of recovery based a posteriori estimator in the superconvergent patch recovery. Superconvergent patch recovery spr technique previously used for error es. The first superconvergent method is superconvergent patch recovery spr method which is developed by zienkiewiczzhu 1,2.
By utilizing the concept of structured mesh refinement using lr bsplines, our aim is to facilitate superconvergence behavior for locally refined meshes as well. The superconvergent patch recovery and a posteriori error. Superconvergent patch recovery and a posteriori error estimation. A type of finite element gradient recovery method based on. Superconvergent patch recovery spr and adaptive finite element refinement, comput. There exist points within the element, namely the gauss integration points, at which the stresses are superconvergent. The method is simple to implement and the numerical results show that it is robust. If you have questions, need help, find a bug or just want to give us feedback you may use this form, or contact us per email research. A modification has been introduced to the new superconvergent patch derivative recovery technique recently developed zienkiewicz and zhu, 1991. The procedure can be classi ed as superconvergent patch recovery. Error analysis for quadtreetype meshcoarsening algorithms. Adaptive eigenfrequency analysis by superconvergent patch.
Other recovery techniques such as the superconvergent patch recovery technique spr8910 or any other improvement of this recovery technique could also be used11 12 14. Spr provides two methods which use the patchrecovery routines. Department of structural mechanics, chalmers university of technology, s. Use these stresses at the gauss integration points to recover nodal stresses that are also superconvergent. The basic principle of this method is recovering element nodal forces by least square fit method analogy on some internal force sample which is known more accurate. Superconvergent patch recovery spr it is well known that for most elements, certain sampling points exist at which the values of o, have a greater accuracy and. Mapping history variables from the old mesh to the new mesh is accomplished by using the recovered. In this method the ips of the old mesh are used as the sampling points. To improve the component of the gradient at a node, an element patch is defined that usually consists of all elements to which the node is connected. The superconvergent patch recovery and a posteriori error estimates.
For nonlinear problems, it is shown that the accuracy and stability of superconvergent patch recovery spr method can be remarkably improved through the modifications introduced in this paper. However, when 4node quadrilateral elements meeting at a node are rigidly rotated with the. Implemented the superconvergent patch recovery stress recovery algorithm. A finite element analysis methodology employing padaptivity is proposed. The technique has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems. The superconvergent patch recovery spr and adaptive finite. In 1992, the superconvergent patch recovery spr method was introduced by zienkiewicz and zhu.
The new submodeling scheme is more convenient in implementation. Mesh adaptivity driven by goaloriented locally equilibrated superconvergent patch recovery o. The superconvergent patch recovery spr and adaptive. It is proved that the method is superconvergent for. The superconvergent patch recovery method spr proposed by. A linear polynomial approximation is obtained by a leastsquares fitting to the finite element solution at certain sample points, which in turn gives the recovered gradient at recovering points. The superconvergent patch recovery spr superconvergent patch recovery method is relative simple and easyused. Application of this method to the 8node serendipity element reveals the existence of two sets of superconvergent points for patch recovery, one of which is the wellknown gaussian points.
Request pdf on researchgate superconvergent patch recovery of finite. Analysis of the superconvergent patch recovery technique. Pdf application of zienkiewiczzhus error estimate with. In addition to these, the recoverbased technique has been also extended to mesh based. The main issue is that i would like the fluxes to be as accurate as possible, which in this case should equate to equal drift and diffusion fluxes, i can simply increase the spatial resolution but this too only helps to a certain degree. A comparative study of stress recovery method and error.
Therefore, any decisionmaking you do about how to start andor implement your recovery plan should take into account your individualized needs and preferences. This software product offers two modes for scanning the system. A new finite element gradient recovery method semantic scholar. On the other hand, we remark that the theoretical properties of this recovery procedure are not very well understood yet, though many theoretical investigations have been carried out in the literature 4, 6, 7, 11, 17, 18. There is even the opportunity to implement these two modes.
May 22, 2007 in this paper, a 3d superconvergent patch recovery spr method is developed for data transferring in elastoplasticity. Since the superconvergent patch scp recovery method is relativity easy to understand and is accurate. The interpolant is available since the exact solution is known. Operating system not showing on system recovery options solution. The superconvergent cluster recovery method the superconvergent cluster recovery method huang, yunqing. Superconvergent patch recovery of gradient field on adaptive meshes is. Improvement of the superconvergent patch recovery technique. In the paper we present a superconvergent patch recovery technique for obtaining higher. The hdd has a recovery partition on it of around 6gb full but i dont. In order to transfer the historydependent variables from old mesh to new one, the internal variables are firstly mapped from the gauss points to nodal points of. Locally equilibrated superconvergent patch recovery for e. In contrast to that technique all flux or stress components are interpolated at the same time, coupled by equilibrium equations at the superconvergent points. For meshes of triangles, we refer to 108 and for how to the apply the results to the.
The superconvergence patch recovery technique and data transfer operators in 3d plasticity problems. Patch recovery based on superconvergent derivatives and equilibrium spre, an enhancement of the superconvergent patch recovery spr, is studied for linear elasticity problems. Superconvergent gradient recovery for virtual element. If the address matches an existing account you will receive an email with instructions to reset your password.
May 25, 2010 a new gradient recovery technique scr superconvergent cluster recovery is proposed and analyzed for finite element methods. This enables us to apply the method to the boundary patches where usually. Famous examples include the simpleweighted averaging 55, superconvergent patch recovery 56,57 spr, and the polynomial preserving recovery 39,40,54 ppr. Were upgrading the acm dl, and would like your input. A linear polynomial approximation is obtained by a leastsquares fitting to the. Mesh adaptivity driven by goaloriented locally equilibrated. A basic fact which bas been used in our study is that the derivative of the finite element method is superconvergent at the gauss points. But sometimes when were trying to use this features, you do notice our hard disk or windows isnt listed here. Efficient finite element methodology based on cartesian grids. The transfer operators are presented for mapping of the state and internal variables between different meshes. Remapping method for transferring data between two meshes.
On the other hand, since there has no concrete recovery schemes been speci ed in step 3, and step 4, almost all the local recovery methods for functions in euclidean domain can be used. Sorry, we are unable to provide the full text but you may find it at the following locations. Hung, a modified superconvergent patch recovery method and its application to large deformation problems. M is assumed as 222 1 23 456 7 8, 1 xn x t mp a m a a a a a aaa.
Using the improved eigenmode in the rayleigh quotient yields an improved eigenvalue. This enhanced spr technique is used to recover both the primal and dual solutions. Hello alain, find attached a paper on acoustic infinite elements will be presented at isma 2004 in leuven. Institute of numerical methods in engineering, university college of swansea, singleton park, swansea sa2 8pp, u. From all recovery techniques we can highlight those based on the superconvergent patch recovery spr technique also developed by zienkiewicz and zhu. Patch recovery based on superconvergent derivatives and. Apr 24, 2018 there are many ways of achieving this, such as superconvergent patch recovery. Superconvergent patch recovery spr the original idea of spr was to improve the gradient value of the computed fe solution at nodal points. A new gradient recovery technique scr superconvergent cluster recovery is proposed and analyzed for finite element methods. On application of two superconvergent recovery procedures to plate. Superconvergence of gradient recovery on deviated discretized. The proposed gradient recovery is formed in three steps.
346 1548 549 524 20 864 47 1288 1175 468 926 1547 587 26 1125 1477 1523 1510 779 1340 1457 1175 1342 845 410 1171 910 1065 410 630 185 898 32 117 970 426 1283 4 757 1136 1486 1417 1189