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Publications (10 of 20) Show all publications
Zhang, Y., Gong, R., Gulliksson, M. & Cheng, X. (2019). A coupled complex boundary expanding compacts method for inverse source problems. Journal of Inverse and Ill-Posed Problems, 27(1), 67-86
Open this publication in new window or tab >>A coupled complex boundary expanding compacts method for inverse source problems
2019 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 27, no 1, p. 67-86Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider an inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary conditions. The unknown source term is to be determined by additional boundary data. This problem is ill-posed since the dimensionality of the boundary is lower than the dimensionality of the inner domain. To overcome the ill-posed nature, using the a priori information (sourcewise representation), and based on the coupled complex boundary method, we propose a coupled complex boundary expanding compacts method (CCBECM). A finite element method is used for the discretization of CCBECM. The regularization properties of CCBECM for both the continuous and discrete versions are proved. Moreover, an a posteriori error estimate of the obtained finite element approximate solution is given and calculated by a projected gradient algorithm. Finally, numerical results show that the proposed method is stable and effective.

Place, publisher, year, edition, pages
Walter de Gruyter, 2019
Keywords
Inverse source problem, expanding compacts method, finite element method, error estimation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:oru:diva-68829 (URN)10.1515/jiip-2017-0002 (DOI)000457195600006 ()2-s2.0-85053166222 (Scopus ID)
Funder
Knowledge Foundation, 20170059
Note

Funding Agencies:

Alexander von Humboldt foundation  

Natural Science Foundation of China  11571311  11401304 

Fundamental Research Funds for the Central Universities  NS2018047 

Available from: 2018-09-11 Created: 2018-09-11 Last updated: 2019-02-13Bibliographically approved
Gulliksson, M. & Mazur, S. (2019). An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection. Computational Economics
Open this publication in new window or tab >>An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection
2019 (English)In: Computational Economics, ISSN 0927-7099, , p. 21Article in journal (Refereed) Epub ahead of print
Abstract [en]

Covariance matrix of the asset returns plays an important role in the portfolioselection. A number of papers is focused on the case when the covariance matrixis positive definite. In this paper, we consider portfolio selection with a singu-lar covariance matrix. We describe an iterative method based on a second orderdamped dynamical systems that solves the linear rank-deficient problem approxi-mately. Since the solution is not unique, we suggest one numerical solution that canbe chosen from the iterates that balances the size of portfolio and the risk. The nu-merical study confirms that the method has good convergence properties and givesa solution as good as or better than the constrained least norm Moore-Penrose solu-tion. Finally, we complement our result with an empirical study where we analyzea portfolio with actual returns listed in S&P 500 index.

Place, publisher, year, edition, pages
Springer, 2019. p. 21
Keywords
Mean-variance portfolio, singular covariance matrix, linear ill-posed problems, second order damped dynamical systems
National Category
Probability Theory and Statistics Economics Other Mathematics
Research subject
Statistics; Economics; Mathematics
Identifiers
urn:nbn:se:oru:diva-74364 (URN)10.1007/s10614-019-09943-6 (DOI)
Available from: 2019-05-22 Created: 2019-05-22 Last updated: 2019-11-18Bibliographically approved
Gulliksson, M., Ögren, M., Oleynik, A. & Zhang, Y. (2019). Damped Dynamical Systems for Solving Equations and Optimization Problems. In: Bharath Sriraman (Ed.), Handbook of the Mathematics of the Arts and Sciences: . Springer
Open this publication in new window or tab >>Damped Dynamical Systems for Solving Equations and Optimization Problems
2019 (English)In: Handbook of the Mathematics of the Arts and Sciences / [ed] Bharath Sriraman, Springer , 2019Chapter in book (Other academic)
Abstract [en]

We present an approach for solving optimization problems with or without constrains which we call Dynamical Functional Particle Method (DFMP). The method consists of formulating the optimization problem as a second order damped dynamical system and then applying symplectic method to solve it numerically. In the first part of the chapter, we give an overview of the method and provide necessary mathematical background. We show that DFPM is a stable, efficient, and given the optimal choice of parameters, competitive method. Optimal parameters are derived for linear systems of equations, linear least squares, and linear eigenvalue problems. A framework for solving nonlinear problems is developed and numerically tested. In the second part, we adopt the method to several important applications such as image analysis, inverse problems for partial differential equations, and quantum physics.  At the end, we present open problems and share some ideas of future work on generalized (nonlinear) eigenvalue problems, handling constraints with reflection, global optimization, and nonlinear ill-posed problems.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Optimization, damped dynamical systems, convex problems, eigenvalue problems, image analysis, inverse problems, quantum physics, Schrödinger equation
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-71881 (URN)10.1007/978-3-319-70658-0 (DOI)978-3-319-70658-0 (ISBN)
Available from: 2019-01-29 Created: 2019-01-29 Last updated: 2019-04-01Bibliographically approved
Baravdish, G., Svensson, O., Gulliksson, M. & Zhang, Y. (2019). Damped second order flow applied to image denoising. IMA Journal of Applied Mathematics, 84(6), 1082-1111
Open this publication in new window or tab >>Damped second order flow applied to image denoising
2019 (English)In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 84, no 6, p. 1082-1111Article in journal (Refereed) Published
Abstract [en]

In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer–Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF.

Place, publisher, year, edition, pages
Oxford University Press, 2019
Keywords
Nonlinear flow, image denoising, p-parabolic, p-Laplace, inverse problems, regularization, damped Hamiltonian system, symplectic method, Störmer–Verlet.
National Category
Computational Mathematics
Identifiers
urn:nbn:se:oru:diva-79218 (URN)10.1093/imamat/hxz027 (DOI)000509388900002 ()
Note

Funding Agency:

Alexander von Humboldt Foundation

 

Available from: 2020-01-16 Created: 2020-01-16 Last updated: 2020-02-06Bibliographically approved
Ögren, M., Jha, D., Dobberschütz, S., Müter, D., Carlsson, M., Gulliksson, M., . . . Sørensen, H. (2019). Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions. Journal of magnetic resonance, 308, Article ID 106597.
Open this publication in new window or tab >>Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions
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2019 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 308, article id 106597Article in journal (Refereed) Published
Abstract [en]

The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In Ögren [Eur. Phys. J. B (2014) 87: 255] local boundary conditions for random walk simulations of NMR relaxation in digital domains were presented. Here, we have applied those boundary conditions to large, three-dimensional (3D) porous media samples. We compared the random walk results with known solutions and then applied them to highly structured 3D domains, from images derived using synchrotron radiation CT scanning of North Sea chalk samples. As expected, there were systematic errors caused by digitalization of the pore surfaces so we quantified those errors, and by using linear local boundary conditions, we were able to significantly improve the output. We also present a technique for treating numerical data prior to input into the ESPRIT algorithm for retrieving Laplace components of time series from NMR data (commonly called T-inversion).

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
NMR-relaxation, random walk, boundary conditions, CT-scanning, T-inversion
National Category
Geophysics Computational Mathematics
Research subject
Physics; Mathematics
Identifiers
urn:nbn:se:oru:diva-76669 (URN)10.1016/j.jmr.2019.106597 (DOI)000495003900019 ()2-s2.0-85072525625 (Scopus ID)
Note

Funding Agencies:

Innovation Fund Denmark through the project P3 - Predicting Petrophysical Parameters  

Maersk Oil through the project P3 - Predicting Petrophysical Parameters 

Available from: 2019-09-23 Created: 2019-09-23 Last updated: 2020-01-16Bibliographically approved
Zhang, Y., Gong, R., Cheng, X. & Gulliksson, M. (2018). A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations. Inverse Problems, 34(6), Article ID 065001.
Open this publication in new window or tab >>A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations
2018 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, no 6, article id 065001Article in journal (Refereed) Published
Abstract [en]

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2018
Keywords
inverse source problems, dynamical system, regularization, convergence, symplectic method
National Category
Computational Mathematics
Identifiers
urn:nbn:se:oru:diva-66813 (URN)10.1088/1361-6420/aaba85 (DOI)000431055900001 ()
Funder
Knowledge Foundation, 20170059
Note

Funding Agencies:

Alexander von Humboldt foundation  

Natural Science Foundation of China  11401304  11571311

Available from: 2018-04-27 Created: 2018-04-27 Last updated: 2018-05-14Bibliographically approved
Cheng, X., Lin, G., Zhang, Y., Gong, R. & Gulliksson, M. (2018). A modified coupled complex boundary method for an inverse chromatography problem. Journal of Inverse and Ill-Posed Problems, 26(1), 33-49
Open this publication in new window or tab >>A modified coupled complex boundary method for an inverse chromatography problem
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2018 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 26, no 1, p. 33-49Article in journal (Refereed) Published
Abstract [en]

Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method.

Place, publisher, year, edition, pages
Walter de Gruyter, 2018
Keywords
Chromatography; adsorption isotherm; inverse problem; coupled complex boundary method; Tikhonov regularization
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-58691 (URN)10.1515/jiip-2016-0057 (DOI)000423813300003 ()
Funder
Swedish Research Council, 2015-04627
Note

Funding Agencies:

NSFC  11571311  11401304 

STINT  IB2015-5989 

KK HOG  20150233 

AForsk  15/497 

Available from: 2017-07-17 Created: 2017-07-17 Last updated: 2018-02-12Bibliographically approved
Lin, G., Zhang, Y., Cheng, X., Gulliksson, M., Forssén, P. & Fornstedt, T. (2018). A regularizing Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography. Applicable Analysis, 97(1), 13-40
Open this publication in new window or tab >>A regularizing Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography
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2018 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 13-40Article in journal (Refereed) Published
Abstract [en]

Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too complex and expensive. The inverse method is a numeric approach for the fast estimation of adsorption isotherms directly from overloaded elution profiles. However, this identification process is usually ill-posed. Moreover, traditional model-based inverse methods are restricted by the need to choose an appropriate adsorption isotherm model prior to estimate, which might be very hard for complicated adsorption behavior. In this study, we develop a Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem. The solvability and convergence for the proposed inverse method are studied. In particular, using a problem-adapted adjoint, we obtain a convergence rate under substantially weaker and more realistic conditions than are required by the general theory. Based on the adjoint technique, a numerical algorithm for solving the proposed optimization problem is developed. Numerical tests for both synthetic and real-world problems are given to show the efficiency of the proposed regularization method.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2018
Keywords
Chromatography; adsorption isotherm; inverse problem; Kohn–Vogelius method; convergence rate
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-55172 (URN)10.1080/00036811.2017.1284311 (DOI)000417831700003 ()2-s2.0-85011298596 (Scopus ID)
Funder
Knowledge Foundation, 20150233Swedish Research Council, 2015-04627
Note

Funding Agencies:

AForsk Foundation  15/497

STINT  IB2015-5989 

NSFC  11571311 

Available from: 2017-02-01 Created: 2017-02-01 Last updated: 2018-01-03Bibliographically approved
Zhang, Y., Fornstedt, T., Gulliksson, M. & Dai, X. (2018). An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data. Inverse Problems in Science and Engineering, 26(10), 1464-1489
Open this publication in new window or tab >>An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data
2018 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 26, no 10, p. 1464-1489Article in journal (Refereed) Published
Abstract [en]

We present here the theoretical results and numerical analysis of a regularization method for the inverse problem of determining the rate constant distribution from biosensor data. The rate constant distribution method is a modern technique to study binding equilibrium and kinetics for chemical reactions. Finding a rate constant distribution from biosensor data can be described as a multidimensional Fredholm integral equation of the first kind, which is a typical ill-posed problem in the sense of J. Hadamard. By combining regularization theory and the goal-oriented adaptive discretization technique,we develop an Adaptive Interaction Distribution Algorithm (AIDA) for the reconstruction of rate constant distributions. The mesh refinement criteria are proposed based on the a posteriori error estimation of the finite element approximation. The stability of the obtained approximate solution with respect to data noise is proven. Finally, numerical tests for both synthetic and real data are given to show the robustness of the AIDA.

Place, publisher, year, edition, pages
Oxfordshire, United Kingdom: Taylor & Francis, 2018
National Category
Computational Mathematics
Identifiers
urn:nbn:se:oru:diva-64002 (URN)10.1080/17415977.2017.1411912 (DOI)000438638300005 ()2-s2.0-85037706652 (Scopus ID)
Funder
Swedish Research Council, 2015-04627
Note

Funding Agencies:

Swedish Knowledge Foundation (KKS) project HOG

AForsk Foundation

Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-08-30Bibliographically approved
Roussou, A., Smyrnakis, I., Magiropoulos, M., Efremidis, N., Kavoulakis, G., Sandin, P., . . . Gulliksson, M. (2018). Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry. New Journal of Physics, 20, Article ID 045006.
Open this publication in new window or tab >>Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry
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2018 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 20, article id 045006Article in journal (Refereed) Published
Abstract [en]

We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2018
Keywords
Bose-Einstein condensation; mixtures; superfluidity; vector solitons
National Category
Computational Mathematics Atom and Molecular Physics and Optics Condensed Matter Physics
Research subject
Physics; Mathematics
Identifiers
urn:nbn:se:oru:diva-65601 (URN)10.1088/1367-2630/aab599 (DOI)000430345700001 ()
Available from: 2018-03-09 Created: 2018-03-09 Last updated: 2018-05-02Bibliographically approved
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