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  • 1.
    Baravdish, G.
    et al.
    Department of Science and Technology, Linköping University, Linköping, Sweden .
    Svensson, O.
    Department of Science and Technology, Linköping University, Linköping, Sweden .
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Zhang, Ye
    Shenzhen MSU-BIT University, 518172 Shenzhen, China; School of Mathematics and Statistics, Beijing Institude of Technology, China.
    Damped second order flow applied to image denoising2019Ingår i: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 84, nr 6, s. 1082-1111Artikel i tidskrift (Refereegranskat)
    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.

  • 2.
    Cheng, Xiaoliang
    et al.
    Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.
    Lin, Guangliang
    Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.
    Zhang, Ye
    Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Mathematics.
    Gong, Rongfang
    Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Mathematics.
    A modified coupled complex boundary method for an inverse chromatography problem2018Ingår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 26, nr 1, s. 33-49Artikel i tidskrift (Refereegranskat)
    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.

  • 3.
    Dai, Xiaoxia
    et al.
    School of Computing Science, Zhejiang University City College, Hangzhou, People’s Republic of China.
    Zhang, Chengwei
    School of Computing Science, Zhejiang University City College, Hangzhou, People’s Republic of China.
    Zhang, Ye
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method2018Ingår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 57, nr 6, s. 2193-2203Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper presents a piecewise constant level set method for the topology optimization of steady Navier- Stokes flow. Combining piecewise constant level set functions and artificial friction force, the optimization problem is formulated and analyzed based on a design variable. The topology sensitivities are computed by the adjoint method based on Lagrangian multipliers. In the optimization procedure, the piecewise constant level set function is updated by a new descent method, without the needing to solve the Hamilton-Jacobi equation. To achieve optimization, the piecewise constant level set method does not track the boundaries between the different materials but instead through the regional division, which can easily create small holes without topological derivatives. Furthermore, we make some attempts to avoid updating the Lagrangian multipliers and to deal with the constraints easily. The algorithm is very simple to implement, and it is possible to obtain the optimal solution by iterating a few steps. Several numerical examples for both two- and three-dimensional problems are provided, to demonstrate the validity and efficiency of the proposed method.

  • 4.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    The Discrete Dynamical Functional Particle Method for Solving Constrained Optimization Problems2017Ingår i: Dolomites Research Notes on Approximation, ISSN 2035-6803, Vol. 10, s. 6-12Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The dynamical functional particle method (DFPM) is a method for solving equations by using a damped second order dynamical system. The dynamical system is solved by a symplectic method that is especially tailored for conservative systems. In this work we have extended DFPM to convex optimization problems with constraints. The method is tested on linear eigenvalue problems with normalization and orthogonallity constraints as well as some simple nonlinear convex optimization problems.

  • 5.
    Gulliksson, Mårten
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Holmbom, Anders
    Department of Engineering and Sustainable Development, Mid-Sweden University, Östersund, Sweden.
    Persson, Jens
    Department of Engineering and Sustainable Development, Mid-Sweden University, Östersund, Sweden.
    Zhang, Ye
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    A separating oscillation method of recovering the G-limit in standard and non-standard homogenization problems2016Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 32, nr 2, artikel-id 025005Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Reconstructing the homogenized coefficient, which is also called the G-limit, in elliptic equations involving heterogeneous media is a typical nonlinear ill-posed inverse problem. In this work, we develop a numerical technique to determine G-limit that does not rely on any periodicity assumption. The approach is a technique that separates the computation of the deviation of the G-limit from the weak -limit of the sequence of coefficients from the latter. Moreover, to tackle the ill-posedness, based on the classical Tikhonov regularization scheme we develop several strategies to regularize the introduced method. Various numerical tests for both standard and non-standard homogenization problems are given to show the efficiency and feasibility of the proposed method.

  • 6.
    Gulliksson, Mårten
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Mazur, Stepan
    Örebro universitet, Handelshögskolan vid Örebro Universitet.
    An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection2019Ingår i: Computational Economics, ISSN 0927-7099, , s. 21Artikel i tidskrift (Refereegranskat)
    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.

  • 7.
    Gulliksson, Mårten
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Oleynik, A.
    Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway.
    Greedy Gauss-Newton algorithms for finding sparse solutions to nonlinear underdetermined systems of equations2017Ingår i: Optimization, ISSN 0233-1934, E-ISSN 1029-4945, Vol. 66, nr 7, s. 1201-1217Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the problem of finding sparse solutions to a system of underdetermined non-linear system of equations. The methods are based on a Gauss-Newton approach with line search where the search direction is found by solving a linearized problem using only a subset of the columns in the Jacobian. The choice of columns in the Jacobian is made through a greedy approach looking at either maximum descent or an approach corresponding to orthogonal matching for linear problems. The methods are shown to be convergent and efficient and outperform the l1 approach on the test problems presented.

  • 8.
    Gulliksson, Mårten
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Ögren, Magnus
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Oleynik, Anna
    Department of Mathematics, University of Bergen, Norway.
    Zhang, Ye
    Faculty of Mathematics, Chemnitz University of Technology, Germany.
    Damped Dynamical Systems for Solving Equations and Optimization Problems2019Ingår i: Handbook of the Mathematics of the Arts and Sciences / [ed] Bharath Sriraman, Springer , 2019Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    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.

  • 9.
    Lin, G.
    et al.
    Department of Mathematics, Zhejiang University, Hangzhou, China.
    Zhang, Ye
    Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Cheng, X.
    Department of Mathematics, Zhejiang University, Hangzhou, China.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Forssén, P.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Fornstedt, T.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    A regularizing Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography2018Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, nr 1, s. 13-40Artikel i tidskrift (Refereegranskat)
    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.

  • 10.
    Lockby, Andreas
    et al.
    School of Science and Technology, Örebro University, Örebro, Sweden..
    Sandin, Patrik
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Ögren, Magnus
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Finding Stationary Solutions of PDEs with Constraints using Damped Dynamical Systems2016Ingår i: Comsol Conference 2016, 2016Konferensbidrag (Refereegranskat)
    Abstract [en]

    The dynamical functional particle method(DFPM) is a method for solving equations, e.g. PDEs, using a second order damped dynamical system. We show how the method can be extended to include constraints both explicitly as global constraints and adding the constraints as additional damped dynamical equations. These methods are implemented in Comsol and we show numerical tests for finding the stationary solution of a nonlinear heat equation with and without constraints (global and dynamical). The results show that DFPM is a very general and robust way of solving PDEs and it should be of interest to implement the approach more generally in Comsol.

  • 11.
    Roussou, Alexandra
    et al.
    Department of Applied Mathematics, University of Crete, Heraklion, Greece.
    Smyrnakis, Ioannis
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, Manolis
    Technological Education Institute of Crete, Heraklion, Greece.
    Efremidis, Nikolaos
    Department of Applied Mathematics, University of Crete, Heraklion, Greece.
    Kavoulakis, Georgios
    Technological Education Institute of Crete, Heraklion, Greece.
    Sandin, Patrik
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Ögren, Magnus
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry2018Ingår i: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 20, artikel-id 045006Artikel i tidskrift (Refereegranskat)
    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.

  • 12.
    Sandin, Patrik
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Ögren, Magnus
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik. Sch Sci & Technol, Univ Örebro, Örebro, Sweden.
    Numerical solution of the stationary multicomponent nonlinear Schrodinger equation with a constraint on the angular momentum2016Ingår i: Physical Review E, ISSN 2470-0045, Vol. 93, nr 3, artikel-id 033301Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We formulate a damped oscillating particle method to solve the stationary nonlinear Schrodinger equation (NLSE). The ground-state solutions are found by a converging damped oscillating evolution equation that can be discretized with symplectic numerical techniques. The method is demonstrated for three different cases: for the single-component NLSE with an attractive self-interaction, for the single-component NLSE with a repulsive self-interaction and a constraint on the angular momentum, and for the two-component NLSE with a constraint on the total angular momentum. We reproduce the so-called yrast curve for the single-component case, described in [A. D. Jackson et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an analogous curve for the two-component NLSE. The numerical results are compared with analytic solutions and competing numerical methods. Our method is well suited to handle a large class of equations and can easily be adapted to further constraints and components.

  • 13.
    Sandin, Patrik
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Ögren, Magnus
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Smyrnakis, J.
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Kavoulakis, G. M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength2017Ingår i: Physical Review E, ISSN 2470-0045, Vol. 95, nr 1, artikel-id 012142Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.

  • 14.
    Zhang, Ye
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Fornstedt, T.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Dai, X.
    School of Computing Science, Zhejiang University City College, Hangzhou, China.
    An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data2018Ingår i: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 26, nr 10, s. 1464-1489Artikel i tidskrift (Refereegranskat)
    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.

  • 15.
    Zhang, Ye
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany.
    Gong, Rongfang
    Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China.
    Cheng, Xiaoliang
    Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations2018Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, nr 6, artikel-id 065001Artikel i tidskrift (Refereegranskat)
    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.

  • 16.
    Zhang, Ye
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany .
    Gong, Rongfang
    Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, P. R. China .
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Cheng, Xiaoliang
    Department of Mathematics, Zhejiang University, Hangzhou, P. R. China.
    A coupled complex boundary expanding compacts method for inverse source problems2019Ingår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 27, nr 1, s. 67-86Artikel i tidskrift (Refereegranskat)
    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.

  • 17.
    Zhang, Ye
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden; .
    Guang-Liang, Lin
    Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China.
    Forssén, Patrik
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Fornstedt, Torgny
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Cheng, Xiao-Liang
    Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China.
    A regularization method for the reconstruction of adsorption isotherms in liquid chromatography2016Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 32, nr 10, artikel-id 105005Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Determining competitive adsorption isotherms is an open problem in liquid chromatography. Since traditional experimental trial-and-error approaches are too complex and expensive, a modern technique of obtaining adsorption isotherms is to solve the inverse problem so that the simulated batch separation coincides with actual experimental results. This is a typical ill-posed problem. Moreover, in almost all cases the observed concentration at the outlet is the total response of all components, which makes the problem more difficult. In this work, we tackle the ill-posedness with a new regularization method, which is based on the fact that the adsorption isotherms do not depend on the injection profile. The proposed method transfers the original problem to an optimization problem with a time-dependent convection–diffusion equation constraint. Iterative algorithms for solving constraint optimization problems for both the equilibrium-dispersive and the transport-dispersive models are developed. The mass transfer resistance is also estimated by the proposed inverse method. A regularization parameter selection method and the convergence property of the proposed algorithm are discussed. Finally, numerical tests for both synthetic problems and real-world problems are given to show the efficiency and feasibility of the proposed regularization method.

  • 18.
    Zhang, Ye
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Hernandez Bennetts, Victor
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Schaffernicht, Erik
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Reconstructing gas distribution maps via an adaptive sparse regularization algorithm2016Ingår i: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 24, nr 7, s. 1186-1204Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we present an algorithm to be used by an inspectionrobot to produce a gas distribution map and localize gas sources ina large complex environment. The robot, equipped with a remotegas sensor, measures the total absorption of a tuned laser beam andreturns integral gas concentrations. A mathematical formulation ofsuch measurement facility is a sequence of Radon transforms,which isa typical ill-posed problem. To tackle the ill-posedness, we developa new regularization method based on the sparse representationproperty of gas sources and the adaptive finite-element method. Inpractice, only a discrete model can be applied, and the quality ofthe gas distributionmap depends on a detailed 3-D world model thatallows us to accurately localize the robot and estimate the paths of thelaser beam. In this work, using the positivity ofmeasurements and theprocess of concentration, we estimate the lower and upper boundsof measurements and the exact continuous model (mapping fromgas distribution to measurements), and then create a more accuratediscrete model of the continuous tomography problem. Based onadaptive sparse regularization, we introduce a new algorithm thatgives us not only a solution map but also a mesh map. The solutionmap more accurately locates gas sources, and the mesh map providesthe real gas distribution map. Moreover, the error estimation of theproposed model is discussed. Numerical tests for both the syntheticproblem and practical problem are given to show the efficiency andfeasibility of the proposed algorithm.

  • 19.
    Zhang, Ye
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Lin, G.
    Department of Mathematics, Zhejiang University, Hangzhou, China.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Forssén, P.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Fornstedt, T.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Cheng, X.
    Department of Mathematics, Zhejiang University, Hangzhou, China.
    An adjoint method in inverse problems of chromatography2017Ingår i: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 25, nr 8, s. 1112-1137Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    How to determine adsorption isotherms is an issue of significant importance in chromatography. A modern technique of obtaining adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides with actual experimental results. In this work, as well as the natural least-square approach, we consider a Kohn–Vogelius type formulation for the reconstruction of adsorption isotherms in chromatography, which converts the original boundary fitting problem into a domain fitting problem. Moreover, using the first momentum regularizing strategy, a new regularization algorithm for both the Equilibrium-Dispersive model and the Transport-Dispersive model is developed. The mass transfer resistance coefficients in the Transport-Dispersive model are also estimated by the proposed inverse method. The computation of the gradients of objective functions for both of the two models is derived by the adjoint method. Finally, numerical simulations for both a synthetic problem and a real-world problem are given to show the robustness of the proposed algorithm.

  • 20.
    Ögren, Magnus
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik. Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark.
    Jha, Diwaker
    Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..
    Dobberschütz, Sören
    Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..
    Müter, Dirk
    Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..
    Carlsson, Marcus
    Center for Mathematical Sciences, Lund University, Lund, Sweden.
    Gulliksson, Mårten
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Stipp, Susan
    Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..
    Sørensen, Henning
    Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..
    Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions2019Ingår i: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 308, artikel-id 106597Artikel i tidskrift (Refereegranskat)
    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).

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