meshless method for solving fixed boundary problem of plasma equilibrium this study solves the grad shafranov equation with a fixed plasma boundary by utilizing a meshless method for the first time previous studies have utilized a finite element method fem to solve an equilibrium inside the fixed separatrix in order to avoid difficulties of fem such as mesh problem difficulty of coding expensive calculation cost this study focuses on the meshless methods especially rbf mfs and kansa s method to solve the fixed boundary problem the results showed that cpu time of the meshless methods was ten to one hundred times shorter than that of fem to obtain the same accuracy

stability of a novel stochastic epidemic model with double epidemic hypothesis abstract in this paper a novel sir disease transmission model is formulated under double epidemic hypothesis and stochastic perturbation we present the stability conditions of the disease free equilibrium of the sir model without stochastic perturbation and with stochastic perturbation we obtain the deterministic stability threshold 1 and 2 of the disease free equilibrium under which the disease free equilibrium is stochastically stable such that the disease will disappear finally leaving all the population susceptible the results show that double epidemic hypothesis and stochastic perturbation have significant effects on the dynamics behaviors of the model

parts of visual form computational aspects underlying recognition is an organization of objects and their parts into classes and hierarchies a representation of parts for recognition requires that they be invariant to rigid transformations robust in the presence of occlusions stable with changes in viewing geometry and be arranged in a hierarchy these constraints are captured in a general framework using notions of a part line and a partitioning scheme a proposed general principle of form from function motivates a particular partitioning scheme involving two types of parts neck based and limb based neck based parts arise from narrowings in shape or the local minima in distance between two points on the boundary while limb based parts arise from a pair of negative curvature minima which have co circular tangents in this paper we present computational support for the limb based and neck based parts by showing that they are invariant robust stable and yield a hierarchy of parts examples illustrate that the resulting decompositions are robust in the presence of occlusion and clutter for a range of man made and natural objects and lead to natural and intuitive parts which can be used for recognition

physics compatible discretization techniques on single and dual grids with application to the poisson equation of volume forms this paper introduces the basic concepts for physics compatible discretization techniques the paper gives a clear distinction between vectors and forms based on the difference between forms and pseudo forms and the operator which switches between the two a dual grid description and a single grid description are presented the dual grid method resembles a staggered finite volume method whereas the single grid approach shows a strong resemblance with a finite element method both approaches are compared for the poisson equation for volume forms by defining a suitably weighted inner product for 1 forms this approach can readily be applied to anisotropic diffusion models for volume forms

direct estimation of the fiber orientation density function from diffusion weighted mri data using spherical deconvolution diffusion weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers the diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel however this model has been shown to fail in regions containing several fiber populations with distinct orientations a number of alternative models have been suggested such as multiple tensor fitting q space and q ball imaging however each of these has inherent limitations in this study we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion weighted mr data without the need for prior assumptions regarding the number of fiber populations present we assume that all white matter fiber bundles in the brain share identical diffusion characteristics thus implicitly assigning any differences in diffusion anisotropy to partial volume effects the diffusion weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function the diffusion weighted attenuation profile for a typical fiber bundle with the fiber orientation density function odf the fiber odf the distribution of fiber orientations within the voxel can therefore be obtained using spherical deconvolution the properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1 5 t clinical scanner the technique can recover the fiber odf in regions of multiple fiber crossing and holds promise for applications such as tractography

the numerical solution of diffusion problems in strongly heterogeneous non isotropic materials a new second order finite difference algorithm for the numerical solution of diffusion problems in strongly heterogeneous and non isotropic media is constructed on problems with rough coefficients or highly nonuniform grids the new algorithm is superior to all other algorithms we have compared it with for problems with smooth coefficients on smooth grids the method is comparable with other second order methods the new algorithm is formulated for logically rectangular grids and is derived using thesupport operators method a key idea in deriving the method was to replace the usual inner product of vector functions by an inner product weighted by the inverse of the material properties tensor and to use the flux operator defined as the material properties tensor times the gradient rather than the gradient as one of the basic first order operators in the support operators method the discrete analog of the flux operator must also be the negative adjoint of the discrete divergence in an inner product that is a discrete analog of the continuum inner product the resulting method is conservative and the discrete analog of the variable coefficient laplacian is symmetric and negative definite on nonuniform grids in addition on any grid the discrete divergence is zero on constant vectors the null space for the gradient is the constant functions and when the material properties are piecewise constant the discrete flux operator is exact for piecewise linear functions we compare the methods on some of the most difficult examples to be found in the literature

an appropriate pest management si model with biological and chemical control concern abstract in this work we consider an si model for pest management and concern about releasing infective pests and spraying pesticides at different fixed moments we prove that all solutions of d s t d t rs t 1 s t i t k s t i t t n l 1 t n d i t d t s t i t wi t t n l 1 t n s t 1 s t t n l 1 i t 2 i t t n l 1 s t 0 t n i t t n 0 l 1 n 1 2 are uniformly ultimately bounded the conditions of the globally asymptotic stability pest extinction boundary periodic solution and the permanence of system are also obtained our results provide reliable tactic basis for the practical pest management

nonlinear analysis of a delayed stage structured predator prey model with impulsive effect and environment pollution abstract in this paper we investigate a stage structured predator prey model with impulsive poisoning and environment pollution sufficient conditions which guaranteed the global attractivity of predator extinction periodic solution and permanence of the system are obtained we believe that the results will provide reliable tactic basis for the practical pest management

a triangular finite element with first derivative continuity applied to fusion mhd applications we describe properties of the reduced quintic triangular finite element the expansion used in the element will represent a complete quartic polynomial in two dimensions and thus the error will be of order h5 if the solution is sufficiently smooth the quintic terms are constrained to enforce c1 continuity across element boundaries allowing their use with partial differential equations involving derivatives up to fourth order there are only three unknowns per node in the global problem which leads to lower rank matrices when compared with other high order methods with similar accuracy but lower order continuity the integrations to form the matrix elements are all done in closed form even for the nonlinear terms the element is shown to be well suited for elliptic problems anisotropic diffusion the grad shafranov schluter equation and the time dependent mhd or extended mhd equations the element is also well suited for 3d calculations when the third angular dimension is represented as a fourier series

analysis of a model of stage structured population dynamics growth with time state dependent time delay the main purpose of this paper is to analyze a model of stage structured population growth where age to maturity is state dependent we found that a positive equilibrium always exists criteria for stability is obtained

completion energies and scale the detection of smooth curves in images and their completion over gaps are two important problems in perceptual grouping we examine the notion of completion energy of curve elements showing and exploiting its intrinsic dependence on length and width scales we introduce a fast method for computing the most likely completion between two elements by developing novel analytic approximations and a fast numerical procedure for computing the curve of least energy we then use our newly developed energies to find the most likely completions in images through a generalized summation of induction fields this is done through multiscale procedures i e separate processing at different scales with some interscale interactions such procedures allow the summation of all induction fields to be done in a total of only o n log n operations where n is the number of pixels in the image more important such procedures yield a more realistic dependence of the induction field on the length and width scales the field of a long element is very different from the sum of the fields of its composing short segments

why starting from differential equations for computational physics the computational methods currently used in physics are based on the discretization of differential equations this is because the computer can only perform algebraic operations the purpose of this paper is to critically review this practice showing how to obtain a purely algebraic formulation of physical laws starting directly from experimental measurements in other words we can get an algebraic formulation avoiding any arbitrary process of discretization of differential equations this formulation has the great merit of maintaining close contact between the mathematical description and the physical phenomenon described

stochastic completion fields a neural model of illusory contour shape and salience we describe an algorithm and representation level theory of illusory contour shape and salience unlike previous theories our model is derived from a single assumption that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane i e the space that one can reasonably assume is represented by neurons of the mammalian visual cortex our model does not employ numerical relaxation or other explicit minimization but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector field convolutions we show that for the random walk we define the maximum likelihood paths are curves of least energy that is on average random walks follow paths commonly assumed to model the shape of illusory contours a computer model is demonstrated on numerous illusory contour stimuli from the literature

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

flow based fiber tracking with diffusion tensor and q ball data validation and comparison to principal diffusion direction techniques in this study we evaluate the performance of a flow based surface evolution fiber tracking algorithm by means of a physical anisotropic diffusion phantom with known connectivity we introduce a novel speed function for surface evolution that is derived from either diffusion tensor dt data high angular resolution diffusion hard data or a combined dt hard hybrid approach we use the model free q ball imaging qbi approach for hard reconstruction the anisotropic diffusion phantom allows us to compare and evaluate the performance of different fiber tracking approaches in the presence of real imaging artifacts noise and subvoxel partial volume averaging of fiber directions the surface evolution approach using the full diffusion tensor as opposed to the principal diffusion direction pdd only is compared to pdd based line propagation fiber tracking additionally dt reconstruction is compared to hard reconstruction for fiber tracking both using surface evolution we show the potential for surface evolution using the full diffusion tensor to map connections in regions of subvoxel partial volume averaging of fiber directions which can be difficult to map with pdd based methods we then show that the fiber tracking results can be improved by using high angular resolution reconstruction of the diffusion orientation distribution function in cases where the diffusion tensor model fits the data poorly

the existence of nonoscillatory solutions to a generalized nonautonomous delay logistic equation sufficient conditions for the existence of nonoscillatory solutions to the delay logistic equation x t r t x t 1 x g t k are obtained where 1

a stage structured holling mass defence predator prey model with impulsive perturbations on predators abstract in this work we consider a stage structured holling mass defence predator prey model with time delay and impulsive transmitting on predators sufficient conditions which guarantee the global attractivity of pest extinction periodic solution and permanence of the system are obtained we also prove that all solutions of the system are uniformly ultimately bounded our results provide reliable tactic basis for the practical pest management

a new stage structured predator prey gomportz model with time delay and impulsive perturbations on the prey abstract in this paper we formulate a robust prey dependent consumption predator prey gomportz model with periodic harvesting catching or poisoning for the prey and stage structure for the predator with constant maturation time delay through stage time delay and perform a systematic mathematical and ecological study by use of the discrete dynamical system determined by the stroboscopic map we obtain a predator extinction periodic solution further we show it is globally attractive when some parameters of the system are under appropriate conditions by using the theory on delay functional and impulsive differential equation we obtain sufficient condition with time delay for the permanence of the system in this paper the main feature is that we introduce time delay and pulse into the predator prey natural enemy pest model with stage structure exhibit a new modeling method which is applied to investigate delay impulsive differential equations and give some reasonable suggestions for pest management

an analysis of finite volume finite element and finite difference methods using some concepts from algebraic topology in this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods illuminating the similarity between the discretization strategies adopted by the two methods in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements we discuss the intrinsic discrete nature of some of the factors appearing in the field equations underlining the exception represented by the constitutive term the discretization of which is maintained as the key issue for numerical methods devoted to field problems we propose a systematic technique to perform this task present a rationale for the adoption of two dual discretization grids and point out some optimization opportunities in the combined selection of interpolation functions and cell geometry for the finite volume method finally we suggest an explanation for the intrinsic limitations of the classical finite difference method in the construction of accurate high order formulas for field problems

a diffusion tensor imaging tractography algorithm based on navier stokes fluid mechanics we introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging dti volumes we customize the navier stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the dti image volume we then estimate the most likely connection paths between points in the dti volume using a metric derived from the fluid velocity vector field we validate our algorithm using digital dti phantoms based on a helical shape our method segmented the structure of the phantom with less distortion than was produced using implementations of heat based partial differential equation pde and streamline based methods in addition our method was able to successfully segment divergent and crossing fiber geometries closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts to assess the performance of our algorithm on anatomical data we applied our method to dti volumes from normal human subjects our method produced paths that were consistent with both known anatomy and directionally encoded color images of the dti dataset

permanence of a stage structured predator prey system with impulsive stocking prey and harvesting predator abstract in this paper we propose a stage structured predator prey system with impulsive stocking immature prey and harvesting predator at different moment we analyze the global attractivity of the mature prey extinction periodic solution and obtain sufficient conditions for the permanence of the system numerical simulations are also inserted to verify the feasibility of the theoretical results moreover the obtained results show that impulsive stocking immature prey or harvesting predator may play a key role on the permanence of the system and provide tactical basis for the biological resources management

a comparison of measures for detecting natural shapes in cluttered backgrounds we propose a new measure of perceptual saliency and quantitatively compare its ability to detect natural shapes in cluttered backgrounds to five previously proposed measures as defined in the new measure the saliency of an edge is the fraction of closed random walks which contain that edge the transition probability matrix defining the random walk between edges is based on a distribution of natural shapes modeled by a stochastic motion each of the saliency measures in our comparison is a function of a set of affinity values assigned to pairs of edges although the authors of each measure define the affinity between a pair of edges somewhat differently all incorporate the gestalt principles of good continuation and proximity in some form in order to make the comparison meaningful we use a single definition of affinity and focus instead on the performance of the different functions for combining affinity values the primary performance criterion is accuracy we compute false positive rates in classifying edges as signal or noise for a large set of test figures in almost every case the new measure significantly outperforms previous measures

euler spiral for shape completion in this paper we address the curve completion problem e g the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion also known as the gap completion or shape completion problem this problem is a significant element of perceptual grouping of edge elements and has been approached by using cubic splines or biarcs which minimize total curvature squared elastica as motivated by a physical analogy our approach is motivated by railroad design methods of the early 1900 s which connect two rail segments by transition curves and by the work of knuth on mathematical typography we propose that in using an energy minimizing solution completion curves should not penalize curvature as in elastica but curvature variation the minimization of total curvature variation leads to an euler spiral solution a curve whose curvature varies linearly with arclength the construction of this curve from a pair of points and tangents at these points is reduced to a nonlinear system of equations involving fresnel integrals whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions since the choice of an appropriate initial curve is critical in this optimization we analytically derive an optimal solution in the class of biarc curves which is then used as the initial curve the resulting interpolations yield intuitive interpolation across gaps and occlusions and are extensible in contrast to scale invariant elastica in addition euler spiral segments can be used in other applications of curve completions e g modeling boundary segments between curvature extrema or skeletal branch geometry

high resolution magnetohydrodynamic equilibrium code for unity beta plasmas there is great interest in the properties of extremely high s magnetohydrodynamic equilibria in axisymmetric toroidal geometry and the stability of such equilibria however few equilibrium codes maintain solid numerical behavior as beta approaches unity the free boundary algorithm presented herein utilizes a numerically stabilized multigrid method current density input position control magnetic axis search and dynamically adjusted simulated annealing this approach yields numerically robust behavior in the spectrum of cases ranging from low to very high s configurations as the convergence time depends linearly on the total number of grid points the production of extremely fine low error equilibria becomes possible such a code facilitates a variety of intriguing applications which include the exploration of the stability of extreme shafranov shift equilibria

filtered multitensor tractography we describe a technique that uses tractography to drive the local fiber model estimation existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit we formulate fiber tracking as recursive estimation at each step of tracing the fiber the current estimate is guided by those previous to do this we perform tractography within a filter framework and use a discrete mixture of gaussian tensors to model the signal starting from a seed point each fiber is traced to its termination using an unscented kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction despite the presence of noise and uncertainty this provides a causal estimate of the local structure at each point along the fiber using two and three fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings in vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization

a ratio dependent predator prey model with disease in the prey in this paper a ratio dependent predator prey system with disease in the prey is formulated and analyzed mathematical analyses of the model equations with regard to invariance of nonnegativity boundedness of solutions nature of equilibria permanence and global stability are analyzed specially we shall show that ratio dependent predator prey models are rich in boundary dynamics and most importantly we shall show that a periodic solution can occur whether the system is permanent or not that is there are solutions which tend to disease free equilibrium while bifurcating periodic solution exists

a new predator prey model with a profitless delay of digestion and impulsive perturbation on the prey abstract in this paper we formulate a robust prey dependent consumption predator prey model with a delay of digestion and impulsive perturbation on the prey using the discrete dynamical system determined by the stroboscopic map we obtain a predator eradication periodic solution and show that the predator eradication periodic solution is globally attractive when harvesting for the prey is over certain value using a new qualitative analysis method for impulsive and delay differential equations we prove the system is uniformly persistent when harvesting for the prey is under certain value further we show the delay of digestion is a profitless time delay moreover we show our theoretical results by numerical simulation in this paper the main feature is that we introduce a delay of digestion and impulsive effects into the predator prey model and exhibit a new mathematical method which is applied to investigate the system which is governed by both impulsive and delay differential equations

radial projection an efficient update rule for relaxation labeling relaxation labeling uses contextual information for finding consistent labelings of graphs although relaxation labeling is parallel and iterative the complexity of updating with standard rules is too costly for practical implementation a description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered this reduction in complexity is achieved by first restricting support vectors to the positive quadrant and then using radial projection onto the constraint instead of normal projection crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions

a fast high order solver for the grad shafranov equation abstract we present a new fast solver to calculate fixed boundary plasma equilibria in toroidally axisymmetric geometries by combining conformal mapping with fourier and integral equation methods on the unit disk we show that high order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives smooth arbitrary plasma cross sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver equilibria with large shafranov shifts can be computed without difficulty spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution a fusion relevant example of an equilibrium with a pressure pedestal is also presented

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

a mimetic spectral element solver for the grad shafranov equation in this work we present a robust and accurate arbitrary order solver for the fixed boundary plasma equilibria in toroidally axisymmetric geometries to achieve this we apply the mimetic spectral element formulation presented in 56 to the solution of the grad shafranov equation this approach combines a finite volume discretization with the mixed finite element method in this way the discrete differential operators can be represented exactly and metric and all approximation errors are present in the constitutive relations the result of this formulation is an arbitrary order method even on highly curved meshes additionally the integral of the toroidal current j is exactly equal to the boundary integral of the poloidal field over the plasma boundary this property can play an important role in the coupling between equilibrium and transport solvers the proposed solver is tested on a varied set of plasma cross sections smooth and with an x point and also for a wide range of pressure and toroidal magnetic flux profiles equilibria accurate up to machine precision are obtained optimal algebraic convergence rates of order p 1 and geometric convergence rates are shown for soloviev solutions including high shafranov shifts field reversed configuration frc solutions and spheromak analytical solutions the robustness of the method is demonstrated for non linear test cases in particular on an equilibrium solution with a pressure pedestal

inferring global perceptual contours from local features we address the problem of contour inference from partial data as obtained from state of the art edge detectors we argue that in order to obtain more pereeptually salient contours it is necessary to impose generic constraints such as continuity and co curvilinearity the implementation is in the form of a convolution with a mask which encodes both the orientation and the strength of the possible continuations we first show how the mask called the extension field is derived then how the contributions from different sites are collected to produce a saliency map we show that the scheme can handle a variety of input data from dot patterns to oriented edgels in a unified manner and demonstrate results on a variety of input stimuli we also present a similar approach to the problem of inferring contours formed by end points in both cases the scheme is non linear non iterative and unified in the sense that all types of input tokens are handled in the same manner

probabilistic streamline q ball tractography using the residual bootstrap q ball imaging has the ability to discriminate multiple intravoxel fiber populations within regions of complex white matter architecture this information can be used for fiber tracking however diffusion mr is susceptible to noise and multiple other sources of uncertainty affecting the measured orientation of fiber bundles the proposed residual bootstrap method utilizes a spherical harmonic representation for high angular resolution diffusion imaging hardi data in order to estimate the uncertainty in multimodal q ball reconstructions the accuracy of the q ball residual bootstrap technique was examined through simulation the residual bootstrap method was then used in combination with q ball imaging to construct a probabilistic streamline fiber tracking algorithm the residual bootstrap q ball fiber tracking algorithm is capable of following the corticospinal tract and corpus callosum through regions of crossing white matter tracts in the centrum semiovale this fiber tracking algorithm is an improvement upon prior diffusion tensor methods and the q ball data can be acquired in a clinically feasible time frame

a finite element method with overlapping meshes for free boundary axisymmetric plasma equilibria in realistic geometries existing finite element implementations for the computation of free boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients as a consequence the location of critical points of the poloidal flux that are of paramount importance in tokamak engineering is constrained to nodes of the mesh leading to undesired jumps in transient problems moreover recent numerical results for the self consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map in this work we propose a mortar element method that employs two overlapping meshes one mesh with cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside the two meshes overlap in a narrow region this approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma while preserving accurate meshing of the geometric details outside this region the continuity of the numerical solution in the region of overlap is weakly enforced by a mortar like mapping

3d stochastic completion fields for mapping connectivity in diffusion mri the 2d stochastic completion field algorithm introduced by williams and jacobs 1 2 uses a directional random walk to model the prior probability of completion curves in the plane this construct has had a powerful impact in computer vision where it has been used to compute the shapes of likely completion curves between edge fragments in visual imagery motivated by these developments we extend the algorithm to 3d using a spherical harmonics basis to achieve a rotation invariant computational solution to the fokker planck equation describing the evolution of the probability density function underlying the model this provides a principled way to compute 3d completion patterns and to derive connectivity measures for orientation data in 3d as arises in 3d tracking motion capture and medical imaging we demonstrate the utility of the approach for the particular case of diffusion magnetic resonance imaging where we derive connectivity maps for synthetic data on a physical phantom and on an in vivo high angular resolution diffusion image of a human brain

bezier surfaces and finite elements for mhd simulations a finite element method based on bicubic bezier surfaces is applied to the simulation of mhd instabilities relevant to magnetically confined fusion the major advantage of the new technique is that it allows a natural way to implement mesh refinement strategy which is not supported by a pure hermite formulation compared to a lagrangian formulation the number of degrees of freedom is significantly reduced the use of an isoparametric representation of the space coordinates allows an accurate alignment of the finite elements to the magnetic field line geometry in a tokamak plasma the bezier finite elements have been implemented in a mhd code using the non linear reduced mhd model in toroidal geometry as an illustration results for soloviev equilibrium and time dependent current hole computations are presented and discussed

nonlinear magnetohydrodynamics simulation using high order finite elements a conforming representation composed of 2d finite elements and finite fourier series is applied to 3d nonlinear non ideal magnetohydrodynamics using a semi implicit time advance the self adjoint semi implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments growth rates for resistive tearing modes with experimentally relevant lundquist number are computed accurately with time steps that are large with respect to the global alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree p two or larger an error diffusion method controls the generation of magnetic divergence error convergence studies show that this approach is effective for continuous basis functions with p 2 where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity is computed accurately with p 3 without mesh alignment a simulation of tearingmode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3d magnetic topologies

computation of mhd equilibrium of tokamak plasma abstract computation of the mhd equilibrium of a tokamak plasma is reviewed as comprehensively as possible the basic equation of this problem is the grad shafranov equation general remarks on this equation and related issues are first summarized with historical survey of the mhd equilibrium solution where some mathematical discussions on the numerical analysis of the problem are also presented distinguishing features of this problem are seen in treatment of the boundary condition and constraining conditions and we describe them in a rather detailed manner in the main part of this review paper we present a concrete description on the numerical procedures of the mhd equilibrium solvers which are classified into two groups that is the real space solvers and the inverse equilibrium solvers we also describe topics on more general equilibrium models that is the equilibrium with steady flow anisotropic equilibria equilibria with specified current sources and equilibrium evolution brief comments on three dimensional equilibrium solvers are also presented as for application of the mhd equilibrium solvers we present only a small part that is beta limit optimization design of external coils analysis of positional instability and analysis of experimentally obtained data from electromagnetic measurement it is concluded that among various kinds of numerical solution methods we can usually find most adequate ones for the present problem