Cascading multi-segment rupture process of the 2023 Turkish earthquake doublet on a complex fault system revealed by teleseismic P wave back projection method

In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks.

Projection and Contraction Methods for Nonlinear Complementarity Problem

We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.

A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations

In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.

PROJECTION METHODS AND APPROXIMATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS

A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.

Velocity Projection with Upwind Scheme Based on the Discontinuous Galerkin Methods for the Two Phase Flow Problem

The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.

Application for Superconvergence of Finite Element Approximations for the Elliptic Problem by Global and Local L²-Projection Methods

Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.

General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems

为一个三步的设计方法的第一个一一般模型被介绍，并且第二，它在 Hilbert 空格设置被用于非线性的变化不平等问题的一个系统的近似解决之可能性。让 H 是一个真实 Hilbert 空格和 K nonempty 被关上 H 的凸的子集。为任意地选择的起始的点 x0 ， y0 ， z0 K ，计算序列 xn ， yxn ， zxn 以便{xn+1=( 1-n-rn ) xn+xPk [ yn-Tyn ] +rnun ，yn=( 1--n ) xn+nPk [ zn-Txn ] +nun ，zn=( 1-an-n ) xn+akPk [ xn-Txn ] +nwn .For ，，> 0 是常数，{ n }，{ n }，{一}，{ rn }，{ n }，{ n } C [ 0,1 ]，{ un }，{ vn }，{ wn }是在 K 的序列，并且 0n + rn 1,0 n + n 1,0 一+ n 1 ，(A) n 0 ，在此 T ：K H 是到 K 上的非线性的印射。最后三步的模型被用于一些变化不平等问题。

SOLVING SYMMETRIC MONOTONE LINEAR VARIATIONAL INEQUALITIES BY SOME MODIFIED LEVITIN-POLYAK PROJECTION METHODS

Abstract Some modified Levitin Polyak projection methods are proposed in this paper for solving monotone linear variational inequalityx∈Ω,(x′-x) T(Hx+c)≤0,\ x′∈Ω.It is pointed out that there are similar methods for solving a general linear variational inequality.

基于Projection VOF方法的熔模铸造蜡模充型过程数值模拟

针对熔模铸造蜡模充型过程数值模拟软件自主开发,建立了流动场和温度场数学模型,采用Cross-WLF粘度模型描述蜡料的流变性能,基于Projection VOF方法进行蜡料流动过程速度场、压力场以及自由表面的求解。通过试验测量获取了K512型蜡料的热物理性能和流变性能的相关数据,拟合得到粘度模型参数。分别在蜡料常粘度和变粘度模型两种条件下对扳机铸件蜡模充型过程进行模拟,结果表明,所建立蜡模充型过程数学模型能较好地描述蜡料的动态流变特性和传热行为。

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

Low side lobe pattern synthesis using projection method with genetic algorithm for truncated cone conformal phased arrays

A hybrid method for synthesizing antenna＇s three dimensional （3D） pattern is proposed to obtain the low sidelobe feature of truncated cone conformal phased arrays. In this method, the elements of truncated cone conformal phased arrays are projected to the tangent plane in one generatrix of the truncated cone. Then two dimensional （2D） Chebyshev amplitude distribution optimization is respectively used in two mutual vertical directions of the tangent plane. According to the location of the elements, the excitation current amplitude distribution of each element on the conformal structure is derived reversely, then the excitation current amplitude is further optimized by using the genetic algorithm （GA）. A truncated cone problem with 8x8 elements on it, and a 3D pattern desired side lobe level （SLL） up to 35 dB, is studied. By using the hybrid method, the optimal goal is accomplished with acceptable CPU time, which indicates that this hybrid method for the low sidelobe synthesis is feasible.

ON THE MONOTONE CONVERGENCE OF THE PROJECTED ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.

Program evaluation and its application to equipment based on super-efficiency DEA and gray relation projection method

For the gray attributes of the equipment program and its difficulty to carry out the quantitative assessment of the equipment program information, the gray relation projection method is simply reviewed. Combining the super-data envelopment analysis（DEA） model and the gray system theory, a new super-DEA for measuring the weight is proposed, and a gray relation projection model is established to rank the equipment programs. Finally, this approach is used to evaluate the equipment program. The results are verified valid and can provide a new way for evaluating the equipment program.

Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L^2 projection method

A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

A Rework Reduction Mechanism in Complex Projects Using Design Structure Matrix Clustering Methods

To reduce the uncertainty and reworks in complex projects,a novel mechanism is systematically developed in this paper based on two classical design structure matrix(DSM)clustering methods:Loop searching method(LSM)and function searching method(FSM).Specifically,the optimal working areas for the two clustering methods are first obtained quantitatively in terms of non-zero fraction(NZF)and singular value modularity index(SMI),in which the whole working area is divided into six sub-zones.Then,a judgement procedure is proposed for conveniently choosing the optimal DSM clustering method,which makes it easy to determine which DSM clustering method performs better for a given case.Subsequently,a conceptual model is constructed to assist project managers in effectively analyzing the network of projects and greatly reducing reworks in complex projects by defining preventive actions.Finally,the aircraft design process is presented to show how the proposed judgement mechanism can be utilized to reduce the reworks in actual projects.

Projected Runge-Kutta methods for constrained Hamiltonian systems

Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation

We study continuous data assimilation(CDA)applied to projection and penalty methods for the Navier-Stokes(NS)equations.Penalty and projection methods are more efficient than consistent Ns discretizations,however are less accurate due to modeling error(penalty)and splitting error(projection).We show analytically and numerically that with measurement data and properly chosen parameters,CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.

CONSTRUCTIONS OF BASES FOR EXTENDED OBLIQUE PROJECTION METHOD

In this paper,we present some sufficient conditions for constructing the bases of the left and the right spaces to ensure the feasibility of the oblique projection method and the extended oblique projection method.