基本信息科学研究教育教学论文专著
基本信息


韩波，男，1963年4月出生，汉族，哈尔滨工业大学数学系教授，博士生导师，哈尔滨工业大学应用数学研究所所长。黑龙江省工业与应用数学学会副理事长。

从1989年开始从事微分方程反问题数值解法及其在科学与工程中的应用研究。近年来，作为主要骨干或负责人先后承担了10项国家自然科学基金重大、重点、面上和专向基金项目的研究工作。先后在国内外学术刊物上发表论文九十余篇，其中SCI论文五十余篇。“微分方程反问题的数值解法及应用”1997年获国家教委科技进步三等奖；“弹性波方程反演方法和弹性波逆散射理论的研究”1998年获航天工业总公司科技进步二等奖；2000年获黑龙江省第五届青年科技奖；“时间推移地震反演及其相关问题”2009年获黑龙江省高校科学技术奖一等奖。

教育经历
1980年-1984年, 黑龙江大学数学系, 学士学位1984年-1987年, 哈尔滨工业大学数学系, 硕士学位1995年-1999年, 哈尔滨工业大学力学系, 博士学位


工作经历


时间工作经历
1987年—1989年哈尔滨工业大学，数学系，助教
1989年—1992年哈尔滨工业大学，数学系，讲师
1992年—1998年哈尔滨工业大学，数学系，副教授
1998年—至今哈尔滨工业大学，数学系，教授
1997年—1998年美国加州大学，Santa Crutz分校，访问学者
2000年—2004年大庆石油管理局和哈尔滨工业大学航天学院，博士后






研究领域
四维地震正反演研究地质雷达资料处理与解释波动方程反问题的小波和多重网格方法双相介质波动方程反演非线性不适定算子方程的多尺度方法 主要研究方向: 微分方程反问题数值解法及其在科学与工程中的应用研究，非线性不适定算子方程数值解法

科研项目

项目名称时间推移地震正、反演的多尺度方法研究

项目来源国家自然科学基金

开始时间2006-01-01

结束时间2006-12-01

担任角色负责
项目类别纵向项目
项目状态完成


项目名称四维地震局域化反演研究

项目来源国家自然科学基金

开始时间2008-01-01

结束时间2010-12-01

担任角色负责
项目类别纵向项目
项目状态完成


项目名称锚杆锚固体系动力参数反演研究

项目来源国家自然科学基金

开始时间2010-01-01

结束时间2010-12-01

担任角色负责
项目类别纵向项目
项目状态完成


项目名称基于稀疏约束与全变差正则化的复杂介质地震波形反演研究

项目来源国家自然科学基金

开始时间2011-01-01

结束时间2013-12-01

担任角色负责
项目类别纵向项目
项目状态完成


项目名称复杂介质四维地震有限元—对比源反演方法研究

项目来源国家自然科学基金

开始时间2013-01-01

结束时间2015-12-01

项目经费70万

担任角色负责
项目类别横向项目
项目状态完成


项目名称复杂介质频率域弹性波方程全波形反演研究

项目来源国家自然科学基金

开始时间2015-01-01

结束时间2018-12-01

项目经费100万

担任角色负责
项目类别横向项目
项目状态完成


奖项成果

奖项名称微分方程反问题的数值解法及应用

获奖时间1997

所获奖项国家教委科技进步三等奖



奖项名称弹性波方程反演方法和弹性波逆散射理论的研究

获奖时间1998

所获奖项航天工业总公司科技进步二等奖



奖项名称黑龙江省第五届青年科技奖

获奖时间2000

所获奖项黑龙江省第五届青年科技奖



奖项名称时间推移地震反演及其相关问题

获奖时间2009

所获奖项黑龙江省高校科学技术奖一等奖



团队成员
陈勇，博士、副教授。研究方向：时间推移地震正反演算法

郭玉坤，博士后、讲师。研究方向：逆散射，地震勘探

李莉，博士、讲师。研究方向：非线性不适定算子方程数值解法，生物医学成像

曹莉，博士、讲师。研究方向：非线性不适定算子方程数值解法，地震勘探

窦以鑫，博士后。研究方向：热传导方程反问题，地球板块运动和地球表面演变耦合效应研究



讲授课程
课程名称

授课对象

总课时数
非线性算子方程数值解

博士生

54
非线性数值分析

硕士生

54
偏微分方程反问题的数值解法

硕士生

36
科学与工程中的反问题

本科生

30




招生信息
硕士招生: 每年招生2名

目前共 人，其中在读3人，已毕业 人


博士招生: 每年招生1-2名

目前共 人，其中在读6人，已毕业 人



论文期刊

论文标题Total variation regularization for the reconstruction of a mountain topography

作者Dou Y.X.，Han B.

期刊名称Applied Numerical Mathematics

期卷62

简单介绍 The aim of this paper is to reconstruct a paleo mountain topography using a total variation (TV) regularization. A coupled system integrates the tectonic process with the surface process to simulate the evolution of a paleo mountain topography. The tectonic process and the surface process are described by a 3D convection-diffusion equation and a 2D convection-diffusion equation, respectively. We recover a piecewise smooth velocity field for the tectonic process as well as reconstruct a piecewise smooth mountain topography for the surface process using a TV regularization in an iterative fashion. The effects of the number of samples and of wavelengths on inversions are investigated. In our numerical experiments, we shall experience three difficulties: (I) recovering a large quantity of information from the limited amount of measurement data: (II) detecting sharp features; (III) choosing a properly initial guess value for a TV regularization. The numerical experiments show that a TV regularization is an efficient and stable algorithm.


论文标题Reconstruction of a velocity field for a 3-D advection-diffusion equation

作者Dou Y.X.，Han B.

期刊名称International Journal of Thermal Sciences

期卷50

简单介绍This work deals with the reconstruction of a piecewise constant velocity field for a 3-D advection-diffusion equation. Reconstructing a velocity field often plays an important role in understanding the formation and evolution of orogenic topography. In order to suppress measurement errors and to identify sharp features, we propose a new regularization integrating an l(1) data fidelity with a total variation(1) penalty term to reconstruct a piecewise constant velocity field. For testing the performance of our proposed regularization method, we compare four different regularization methods. From numerical experiments, we can draw conclusions: (I) an l(1) data fidelity can suppress measurement errors including Gaussian noise and non-Gaussian noise; (II) a total variation penalty term has the ability to identify sharp features.


论文标题The finite difference method for dissipative Klein-Gordon-Schrodinger equations in three space dimensions

作者Zhang F.Y., Han B.

期刊名称Journal of Computational Mathematics

期卷28

简单介绍A fully discrete finite difference scheme for dissipative Klein-Gordon-Schrodinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding theorems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in H(2) x H(2) x H(1) over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.


论文标题A level set method for the inverse problem of wave equation in the fluid-saturated porous media

作者 He Y., Han B.

期刊名称Commun. Comput.Phys.

期卷6

简单介绍In this paper, a level set method is applied to the inverse problem of 2-D wave equation in the fluid-saturated media. We only consider the situation that the parameter to be recovered takes two different values, which leads to a shape reconstruction problem. A level set function is used to present the discontinuous parameter, and a regularization functional is applied to the level set function for the ill-posed problem. Then the resulting inverse problem with respect to the level set function is solved by using the damped Gauss-Newton method. Numerical experiments show that the method can recover parameter with complicated geometry and the noise in the observation data.


论文标题An implicit Landweber method for nonlinear ill-posed operator equations

作者 Wang W., Han B.

期刊名称J. Comput. Appl. Math.

期卷230

简单介绍In this paper, we are interested in the solution of nonlinear inverse problems of the form F(x) = y. We propose an implicit Landweber method, which is similar to the third-order midpoint Newton method in form, and consider the convergence behavior of the implicit Landweber method. Using the discrepancy principle as a stopping criterion, we obtain a regularization method for ill-posed problems. We conclude with numerical examples confirming the theoretical results, including comparisons with the classical Landweber iteration and presented modified Landweber methods.


论文标题A wavelet multiscale method for inversion of Maxwell equation

作者L.Ding, B.Han, J.Q.Liu

期刊名称Appl. Math. Mech.

期卷30

简单介绍This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.


论文标题The Hamiltonian structure of the expanding integrable model of the generalized AKNS hierarchy

作者B.L.Feng, B.Han

期刊名称Chaos, Solitons & Fractals

期卷39

简单介绍With the help of a new loop algebra (g) over bar, it simple deducing method for the generalized AKNS hierarchy (briefly called GAH) is given. Then, (g) over bar is extended to a larger loop algebra (G) over tilde from which the integrable couplings of the GAH, i.e. a kind of expanding integrable model, is obtained. It follows that its Hamiltonian structure is worked out by making use of the quadratic-form identity. Finally, it subalgebra (a) over bar (3) of the loop algebra (A) over bar (3) is devoted to getting the conserved densities of the integrable couplings by the HAKS algorithm.


论文标题A wavelet adaptive-homotopy method for inverse problem in the fluid-saturated porous media

作者Y.He, B.Han

期刊名称Appl. Math. Comput.

期卷208

简单介绍In this paper, we consider a parameter identification problem for the elastic wave equations in the fluid-saturated porous media. A wavelet adaptive-homotopy method is proposed for the recovery of porosity. This algorithm combines the wavelet multiscale inversion idea with the adaptive-homotopy method. And the adaptive-homotopy method provides a simple way to adapt computational refinement to the choice of the homotopy parameter. Numerical results illustrate that the wavelet adaptive-homotopy method is globally convergent and highly effective for solving the inverse problem.


论文标题A homotopy-projection method for the parameter estimation problems

作者Y.Liu,B.Han,Y.X.Dou

期刊名称Inverse Problems in Science and Engineering

期卷16

简单介绍A homotopy-projection method is proposed for the parameter estimation problems of partial differential equations. To overcome the local convergence of traditional iterative methods, the homotopy method and Tikhonov regularization combine to form a new and widely convergent method. Additionally to that, projection method is introduced to fulfill the constrains described by a closed and convex set. As a practical application, the parameter estimation problem of an elliptic equation is solved. Numerical results show the method@#%s effectiveness.


论文标题A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

作者Y.He,B.Han

期刊名称Appl.Math.Mech.

期卷29

简单介绍 In this paper, we consider numerical simulation of wave propagation in fluid-saturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.


论文标题A R-K type modified Landweber method for nonlinear ill-posed operator equations

作者W.Wang, B.Han, L.Li

期刊名称J.Comput. Appl. Math.

期卷212

简单介绍In this paper, we investigate the convergence behavior of a Runge-Kutta type modified Landweber method for nonlinear ill-posed operator equations. In order to improve the stability and convergence of the Landweber iteration, a 2-stage Gauss-type Runge-Kutta method is applied to the continuous analogy of the modified Landweber method, to give a new modified Landweber method, called R-K type modified Landweber method. Under some appropriate conditions, we prove the convergence of the proposed method. We conclude with a numerical example confirming the theoretical results, including comparisons to the modified Landweber iteration.


论文标题A dynamical system method for solving nonlinear ill-posed problems

作者L.Li, B.Han

期刊名称Appl.Math.Comput.

期卷197

简单介绍This paper investigates the dynamical systems for solving nonlinear ill-posed problems, and uses Lyapunov theory which is constructed in this paper to prove the stability of the solution of the dynamical system problems. Finally, numerical experiments are presented with PC-MATLAB.


论文标题A new method for solving a class of singular two-point boundary value problems

作者Wenyan Wang,Minggen Cui, Bo Han

期刊名称Appl.Math.Comput.

期卷206

简单介绍In this paper, we present a new method for solving a class of singular two-point boundary value problems for certain ordinary differential equations having singular coefficients. The exact solution u(x) is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution u(n)(x) is obtained by solving a linear system of equations and is proved to converge to the exact solution. This method can avoid the Gram-Schmidt orthogonalization process, so as to improve the precision and decrease consumedly the runtime when the number of knots is the same, especially when the number of knots is large. It is efficiently applied to solve some model problems with the comparison between the numerical solutions and the exact solutions. The high precision of this method is demonstrated by the numerical examples.


论文标题R-K type Landweber method for nonlinear ill-posed problems

作者L.Li, B.Han, W.Wang

期刊名称J.Comput.Appl.Math.

期卷206

简单介绍In this paper we propose the R-K type Landweber iteration and investigate the convergence of the method for nonlinear ill-posed problem F(x) = y where F : H -> H is a nonlinear operator between Hilbert space H. Moreover, for perturbed data with noise level delta we prove that the convergence rate is O(delta(2/3)) under appropriate conditions. Finally, the numerical performance of this R-K type Landweber iteration for a nonlinear convolution equation is compared with the Landweber iteration.


论文标题A wavelet multiscale-homotopy method for the inverse problem of two-dimensional acoustic wave equation

作者H.S.Fu and B.Han

期刊名称Appl.Math.Comput.

期卷190

简单介绍By introducing the wavelet multiscale method and the homotopy method to the inversion process for the velocity estimation problem of two-dimensional acoustic wave equation in seismic prospecting, a joint inversion method-wavelet multiscale-homotopy method is designed, which is stable, globally convergent, and has the ability of noise suppression. The results of numerical simulations and noise suppression tests indicate our method@#%s effectiveness.


论文标题The double integrable couplings of tu hierarchy

作者B.L.Feng, B.Han, Y.Wei

期刊名称Commun. Theor. Phys.

期卷48

简单介绍Two types of Lie algebras are presented, from which two integrable couplings associated with the Tu isospectral problem are obtained, respectively. One of them possesses the Hamiltonian structure generated by a linear isomorphism and the quadratic-form identity. An approach for working out the double integrable couplings of the same integrable system is presented in the paper.


论文标题A widely convergent generalized pulse-spectrum technique for the inversion of two-dimensional acoustic wave equation

作者B.Han，G.F.Feng，J.Q.Liu

期刊名称Appl.Math.Comput.

期卷172

简单介绍An algorithm of the generalized pulse-spectrum technique (GPST) is used for the inverse problems of two-dimensional acoustic wave equation, and a skill of saving computational cost is designed in choosing regularizing parameters. To overcome the defect of the local convergence of the GPST, a widely convergent GPST (WCGPST) is constructed. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the WCGPST. It is found that the WCGPST is not only as robust as the standard GPST but also possessing widely convergent region.


论文标题A homotopy method for the inversion of a two-dimensional acoustic wave equation

作者B. Han, H. S. Fu, Z. Li

期刊名称Inverse problems in Science and Engineering

期卷13

简单介绍This article considers the problem of estimating the velocity in a two-dimensional acoustic wave equation. In order to overcome the defects of local convergence of conventional methods, a general homotopy inversion strategy is proposed for the continuous inverse model. On the basis of this strategy, a practical algorithm is constructed by introducing Tikhonov regularization method for the nonlinear operator equation which is obtained from the discretization of the continuous inverse model. Numerical simulations show that the algorithm is a fast and widely convergent inversion method.


论文标题Electrical resistivity tomography by using a hybrid regularization

作者B.Han,Y.X.Dou,L.Ding

期刊名称Chinese J.Geophys.-Chinese edition

期卷55(3)

简单介绍In this paper, we investigate the reconstruction of a piecewise constant resistivity in 2D by using a hybrid regularization. This hybrid regularization integrates a total variation (TV) regularization with a classical Tikhonov regularization. A TV regularization can reconstruct a piecewise constant resistivity as well as detect jump boundaries, and a classical Tikhonov regularization has the ability to reconstruct a smooth resistivity. Combining a classical Tikhonov regularization with a TV regularization, we can see that the hybrid regularization improves the results of numerical experiments.


论文标题Inversion imaging method for concrete non-destructive testing based on GPR

作者L.Ding,B.Han,R.Z.Liu

期刊名称Chinese J.Geophys.-Chinese Edition

期卷55(1)

简单介绍In this paper, we propose a new inversion imaging method for concrete non-destructive testing in hydropower engineering. Traditional method depends largely on one@#%s experience to observe the offset detection data, its accuracy can not be guaranteed. This method is based on the electromagnetic field theory, and uses GPR (Ground Penetrating Radar) as the detecting means. According to GPR data, we give the inversion algorithm which is a homotopy method coupled with fast convergent damping Gauss-Newton method, the imaging results are quantitative and visualized. This method overcomes the shortcomings that traditional GPR profile only roughly reflects the depth and size of concrete defect, it can not only accurately detect the position but also the size and property of defect. Numerical simulations and processing of actual data verified that the inversion imaging results are visualized, reliable and practical.


论文标题Numerical inversion of reconstruction of mountain surface by homotopy method

作者Y.X.Dou,B.Han

期刊名称Chinese J.Geophys.-Chinese edition

期卷54(7)

简单介绍 In this paper, we focus on the reconstruction of a mountain surface with time span of millions of years. Reconstruction of a mountain surface consists of two processes. One is the heat transport process model in three dimensional spatial domain, which describes the change of temperature of rocks, and the other is the surface process model in two dimensional spatial domain, which explains the evolution of mountain surface. This is a large scale nonlinear optimization for reconstruction of a mountain surface back to millions of years. To overcome the strong dependency on initial guess value and multiple local minima, we apply a homotopy method to restore the mountain surface. Numerical results show that our algorithm has a good convergent property for given initial guess values and is robust.


论文标题Convergence analysis of the homotopy perturbation method for solving nonlinear ill-posed operator equations

作者L.Cao,B.Han

期刊名称Computers & Mathematics with Applications

期卷61(8)

简单介绍The homotopy perturbation method is used to construct a new iteration algorithm for solving nonlinear ill-posed operator equations. Numerical tests are given, showing that the algorithm is more efficient than the well-known Landweber method.


论文标题Multiscale total variation method and its application on time-lapse seismiv

作者Y.Chen,B.Han,L.Xiao

期刊名称Chinese J.Geophys.-Chinese edition

期卷53(8)

简单介绍 In this paper, a multiscale total variation method is applied to parameter identification problems for time-lapse seismic which consists of two or more seismic surveys shooting at different calendars. For the discontinuous parameters, a total variation regularization method is introduced instead of the traditional Tikhonov regularization. Combined with a multiscale method,a multiscale total variation regularization method is put forward to improve computational efficiency and accuracy. In numerical simulation, the multiscale total variation regularization method is compared with both the multiscale-Tikhonov regularization method and a single scale total variation regularization method for time-lapse seismic inversion. The numerical results show that the proposed multiscale total variation method is more stable, faster and more accurate than other methods.


论文标题Homotopy perturation method for nonlinear ill-posed operator equations

作者L.Cao,B.Han,W.Wang

期刊名称Int.J.Nonlin.Sci.Numer.Simul.

期卷10(10)



论文标题A homotopy method for well-log constraint waveform inversion

作者B.Han,H.S.Fu,H.Liu

期刊名称Geophysics

期卷72(1)

简单介绍The primary difficulty posed by the method of waveform inversion for the acoustic-wave equation is the presence of local minima of the objective function. Waveform inversion fails to converge to the global minimum unless the wavefield contains very low frequencies, or the starting model is very close to the true model. Constraints can improve the convergence of the method; however, if the starting model is far from the correct model, normal iterative methods will still get trapped in local minima. We designed a homotopy method to improve the robustness of waveform inversion; it makes natural use of constraints, such as well logs. In addition, to further condition the inverse problem, we incorporate standard Tikhonov regularization. We demonstrate through a synthetic example that our method is more likely to find a global minimum than normal iterative methods.


论文标题A wavelet multiscale iterative regularization method for the parameter estimation problems of partial differential equations

作者H.S.Fu,B.Han,H.B.Liu

期刊名称Neurocomputing

期卷Vol.104



论文标题Inverse heat problem of determining time-dependent source parameter in reproducing kernel space

作者Wenyan Wang,Bo Han,Masahiro Yamamoto

期刊名称Nonlinear Analysis-Real World Applications

期卷Vol.14



论文标题Regularization method with sparsity constrains for seismic waveform inversion

作者Wang Wei,han Bo,Tang Jinping

期刊名称Chinese Journal of Geophysics-Chinese Edition

期卷Vol.56



论文标题A homotopy perturbation method for well log constrained seismic inversion

作者Fu Hongsun,Cao Li,Han Bo

期刊名称Chinese Journal of Geophysics-Chinese Edition

期卷Vol.55



论文标题Split Bregman iterative algorithm for sparse reconstruction of electrical impedance tomography

作者J.Wang,J.W.Ma,B.Han

期刊名称Signal Processing

期卷Vol.92



论文标题A theoretical study for RTE-based parameter identification problems

作者Jinping Tang,Weimin Han,Bo Han

期刊名称Inverse Problems

期卷Vol.29



论文标题Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation

作者Wenyan Wang,Masahiro Yamamoto,Bo han

期刊名称Inverse Problems

期卷Vol.29



出版物

出版物名称非线性不适定算子方程数值解法

作者韩波，李莉

出版时间,完成时间2011-01-01

出版社科学出版社