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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：3D Fracture Development Analysis with A Modified XFEM
XFEM 三维裂缝 发育分析
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2023/11/6
扩展有限元法(XFEM)是目前裂纹分析的主流数值方法。2009年起，ABAQUS、ANSYS等主流商业软件集成XFEM并应用于裂纹问题，标志着该方法被工业界广泛接受。然而，在实际应用中XFEM仍然受到两方面的困扰：总体方程高度病态和动力学计算时能量难以守恒。基于“困难的根源在于单位分解插值引入的额外自由度”这一判断和认识，我们提出了一种无额外自由度的改进型扩展有限元方法，有效解决了现有方法总体刚度...
2017 PKU Workshop on Computation and Big Data Analysis
2017 PKU Workshop Computation and Big Data Analysis
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2017/3/28
The rapid growth of data starts to inflict a major impact in many fields such as computational mathematics, optimization, statistics, computer science, etc. Big data analysis is a new and exciting dir...
Robust efficient frontier analysis with a separable uncertainty model
The mean - variance model effective portfolio construction model parameters return on assets uncertainty analysis and numerical examples
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2015/8/10
Mean-variance (MV) analysis is often sensitive to model mis-specification or uncertainty, meaning that the MV efficient portfolios constructed with an estimate of the model parameters (i.e., the expec...
An Extended Multistep Shanks Transformation and Convergence Acceleration Algorithm With Their Convergence and Stability Analysis
convergence acceleration algorithm integrable system molecule solution conver- gence stability
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2012/8/10
The molecule solution of an extended discrete Lotka-Volterra equation is constructed,
from which a new sequence transformation is proposed. A convergence acceleration algorithm for
implementing this...
Gradient Flow Based Semi-implicit Finite Element Method and its Convergence Analysis for Image Reconstruction
Gradient flow, Finite element method, Convergence analysis, Image reconstruction
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2012/8/10
In this paper, we present a novel L2-gradient flow based semi-implicit finite element
method for solving a variational model of image reconstruction under various data scenarios,
especially for the ...
Flexible Multi-scale Image Alignment Using B-Spline Reparametrization -Theoretical Analysis
Flexible alignment L2-gradient flow Bi-cubic B-spline Existence and uniqueness System of ordinary differential equations
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2012/8/10
In the first part of this companion volumes, we present a new flexible alignment model and
an iterative algorithm based on an L2-gradient flow. In this second part of the companion
volumes, we focus...
Distribution of Zeros of Mittag-Leffler Function and Relevant Spectrum Analysis
Eigenvalue of Operator Fractional Derivative Mittag-LefflerFunction Spectrum Analysis
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2012/8/10
This paper is devoted to the distribution of eigenvalues of op-
erators generated by differential expressions of fractional order with Sturm-
Liouville regional conditions. In particular it offers a...
Analysis Of A One-Dimensional Nonlocal Quasicontinuum Method
Quasicontinuum method ghost force geometrically consistent scheme
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2012/8/10
The accuracy of the quasicontinuum method is analyzed using a series of models
with increasing complexity. It is demonstrated that the existence of the ghost force may lead to large
errors. It is al...
Analysis of the Heterogeneous Multiscale Method for Parabolic Homogenization Problems
Analysis the Heterogeneous Multiscale Method Parabolic Homogenization
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2012/8/7
The heterogeneous multiscale method (HMM) is applied to various parabolic problems
with multiscale coefficients. These problems can be either linear or nonlinear. Optimal
estimates are proved for th...
A posteriori error analysis for a continuous space-time finite element method for a hyperbolic integro-differential equation
integro-differential equation continuous Galerkin finite element method convolution kernel stability a posteriori estimate
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2012/5/9
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error repres...
Numerical Analysis of Parallel Replica Dynamics
Numerical Analysis Parallel Replica Dynamics Numerical Analysis
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2012/4/23
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. Such processes spend much of their time about the minima of an und...
Convergence analysis of a multigrid algorithm for the acoustic single layer equation
Convergence analysis multigrid algorithm acoustic single layer equation
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2012/2/29
We present and analyze a multigrid algorithm for the acoustic single layer equation in two dimensions. The boundary element formulation of the equation is based on piecewise constant test functions an...
First Order Convergence Analysis for Sparse Grid Method in Stochastic Two-Stage Linear Optimization Problem
Convergence Analysis Stochastic Optimization Scenario Generation Convex Analysis Measure Theory
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2013/1/30
Stochastic two-stage linear optimization is an important and widely used optimization model. Efficiency of numerical integration of the second stage value function is critical. However, the second sta...
Context-Dependent Data Envelopment Analysis with Interval Data
DEA Context-Dependent Interval Data Interval Attractiveness Interval Progress
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2013/1/30
Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative efficiency of decision making units (DMUs) on the basis of multiple inputs and outputs. The context-dependent DEA...
Convergence Analysis of Meshfree Approximation Schemes
Meshfree Approximation Schemes Numerical Analysis
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2011/9/29
Abstract: This work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the Local Maximum-Entropy (LME) sch...