A finite volume method for global electromagnetic induction forward modeling on collocated unstructured grids

Global electromagnetic induction provides an efficient way to probe the electrical conductivity in the Earth’s deep interior.Owing to the increasing geomagnetic data especially from high-accuracy geomagnetic satellites,inverting the Earth’s three-dimensional conductivity distribution on a global scale becomes attainable.A key requirement in the global conductivity inversion is to have a forward solver with high-accuracy and efficiency.In this study,a finite volume method for global electromagnetic induction forward modeling is developed based on unstructured grids.Arbitrary polyhedral grids are supported in our algorithms to obtain high geometric adaptability.We employ a cell-centered collocated variable arrangement which allows convenient discretization for complex geometries and straightforward implementation of multigrid technique.To validate the method,we test our code with two synthetic models and compare our finite volume results with an analytical solution and a finite element numerical solution.Good agreements are observed between our solution and other results,indicating acceptable accuracy of the proposed method.

An adaptive finite-difference method for seismic traveltime modeling based on 3D eikonal equation

3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.

Integrated multi-scale approach combining global homogenization and local refinement for multi-field analysis of high-temperature superconducting composite magnets

Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.

A New Class of Nonlinear Conjugate Gradient Methods with Global Convergence Properties

非线性共轭梯度法由于其迭代简单和储存量小,且搜索方向不需要满足正割条件,在求解大规模无约束优化问题时占据及其重要的地位.提出了一类新的共轭梯度法,其搜索方向是目标函数的下降方向.若假设目标函数连续可微且梯度满足Lipschitz条件,线性搜索满足Wolfe原则,讨论了所设计算法的全局收敛性.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

探讨无约束优化的一族最优条件数自调比变尺度（ＯＣＳＳＶＭ）算法的收敛性。证明了采用Ｗｏｌｆｅ线性搜索的此族算法对于一般的凸函数是整体收敛的。

GLOBAL COVERGENCE OF THE NON-QUASI-NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.

Global quasi-minimal residual method for the Sylvester equations

In this paper, a global quasi-minimal residual （QMR） method was presented for solving the Sylvester equations. Some properties were investigated with a new matrix product for the global QMR method. Numerical results with the global QMR and GMRES methods compared with the block GMRES method were given. The results show that the global QMR method is less time-consuming than the global GMRES （generalized minimal residual） and block GMRES methods in some cases.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

A GLOBAL LINEAR AND LOCAL QUADRATIC SINGLE-STEP NONINTERIOR CONTINUATION METHOD FOR MONOTONE SEMIDEFINITE COMPLEMENTARITY PROBLEMS

A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.

A FILTER-TRUST-REGION METHOD FOR LC^1 UNCONSTRAINED OPTIMIZATION AND ITS GLOBAL CONVERGENCE

In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.

An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

Numerical simulation of the welding deformation for the side sill of the bogie frame based on local-global method

Considering the limitation of computational capacity, a new finite element solution is used to simulate the welding deformation of the side sill of railroad car＇ s bogie frame based on the local-global method. Firstly, a volumetric heat source defined by a double ellipsoid is adopted to simulate the thermal distributions of the arc welding process. And then, the local models extracted from the global model are computed with refined meshes. On these bases, the global distortions of the subject studied are ascertained by transferring the inner forces of computed local models to the global model. It indicates that the local-global method is feasible for simulating the large welded structures by comparing the computed results with the corresponding actual measured values. The work provides basis for optimizing the welding sequence and clamping conditions, and has theoretical values and engineering significance in the integral design, manufacturing technique selection of the bogie frame, as well as other kinds of large welded structures.

A GLOBALLY AND SUPERLINEARLY CONVERGENT TRUST REGION METHOD FOR LC^1 OPTIMIZATION PROBLEMS

A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.

A Globally Convergent Polak-Ribiere-Polyak Conjugate Gradient Method with Armijo-Type Line Search

In this paper, we propose a globally convergent Polak-Ribiere-Polyak (PRP) conjugate gradient method for nonconvex minimization of differentiable functions by employing an Armijo-type line search which is simpler and less demanding than those defined in [4,10]. A favorite property of this method is that we can choose the initial stepsize as the one-dimensional minimizer of a quadratic modelΦ(t):= f(xk)+tgkTdk+(1/2) t2dkTQkdk, where Qk is a positive definite matrix that carries some second order information of the objective function f. So, this line search may make the stepsize tk more easily accepted. Preliminary numerical results show that this method is efficient.

STRAIGHTFORWARD MULTI-SCALE BOUNDARY ELEMENT METHOD FOR GLOBAL/LOCAL MECHANICAL ANALYSIS OF ELASTIC HETEROGENEOUS MATERIAL

A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.

ON THE GLOBAL CONVERGENCE OF CONJUGATE GRADIENT METHODS WITH INEXACT LINESEARCH

In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.

GLOBAL CONVERGENCE OF THE GENERAL THREE TERM CONJUGATE GRADIENT METHODS WITH THE RELAXED STRONG WOLFE LINE SEARCH

The global convergence of the general three term conjugate gradient methods with the relaxed strong Wolfe line search is proved.

Hybrid method for global optimization using more accuracy interval computation

In this paper, a novel hybrid method is presented for finding global optimization of an objective function. Based on the interval computation, this hybrid method combines interval deterministic method and stochastic evolution method. It can find global optimization quickly while ensuring the deterministic and stability of the algorithm. When using interval computation, extra width constraints accuracy of interval computation results. In this paper, a splitting method to reduce the extra width is introduced. This method is easy and it can get a more precise interval computation result. When finding the global optimization, it can increase the efficiency of pruning. Several experiments are given to illustrate the advantage of the new hybrid method.

GLOBAL LINEAR AND QUADRATIC ONE-STEP SMOOTHING NEWTON METHOD FOR VERTICAL LINEAR COMPLEMENTARITY PROBLEMS

A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).

Global Convergence of a Hybrid Conjugate Gradient Method

Conjugate gradient method is one of successful methods for solving the unconstrained optimization problems. In this paper, absorbing the advantages of FR and CD methods, a hybrid conjugate gradient method is proposed. Under the general Wolfe linear searches, the proposed method can generate the sufficient descent direction at each iterate,and its global convergence property also can be established. Some preliminary numerical results show that the proposed method is effective and stable for the given test problems.