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  • 1.
    Abrahamsson, Fredrik
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Strong L1 convergence to equilibrium without entropy conditions for the Boltzmann equation1999Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 24, nr 7-8, s. 1501-1535Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The main result of this paper is that for the har dsphere kernel, the solution of the spatially homogenous Boltzmann equation converges strongly in L1 to equilibrium given that the initial data f0 belongs to L1(R3,(1+v^2)dv). This was previously known to be true with the additional assumption that f0logf0 belonged to L1(R3), which corresponds to bounded initial entropy.

  • 2.
    Abrahamsson, Fredrik
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Strong L1 convergence to equilibrium without entropy conditions for the spatially homogenous Boltzmann equation1997Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    This paper deals with solutions to the Cauchy problem for the spatially homogeneous non-linear Boltzmann equation. The main result is that for the hard sphere kernel, a solution to the Boltzmann equation converges strongly in L1 to equilibrium given that the initial data f0 belongs to L1(R^3;(1+v^2)dv). This was previously known to be true with the additional assumption that f0logf0 belonged to L1(R^3). For the proof of the main theorem, new regularising effects for the gain term in the collision operator are derived, and previous results concerning uniform bounds on the time it takes for a solution to the Boltzmann equation to reach equilibrium are extended.

  • 3.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    A modified Schwarz-Christoffel mapping for regions with piecewise smooth boundaries2008Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 213, nr 1, s. 56-70Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A method where polygon corners in Schwarz-Christoffel mappings are rounded, is used to construct mappings from the upper half-plane to regions bounded by arbitrary piecewise smooth curves. From a given curve, a polygon is constructed by taking tangents to the curve in a number of carefully chosen so called tangent points. The Schwarz-Christoffel mapping for that polygon is then constructed and modified to round the corners.Since such a modification causes effects on the polygon outside the rounded corners, the parameters in the mapping have to be re-determined. This is done by comparing side-lengths in tangent polygons to the given curve and the curve produced by the modified Schwarz-Christoffel mapping. The set of equations that this comparison gives, can normally be solved using a quasi--Newton method.The resulting function maps the upper half--plane on a region bounded by a curve that apart from possible vertices is smooth, i.e., one time continuously differentiable, that passes through the tangent points on the given curve, has the same direction as the given curve in these points and changes direction monotonically between them. Furthermore, where the original curve has a vertex, the constructed curve has a vertex with the same inner angle.The method is especially useful for unbounded regions with smooth boundary curves that pass infinity as straight lines, such as channels with parallel walls at the ends. These properties are kept in the region produced by the constructed mapping.

  • 4.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Modified Schwarz-Christoffel mappings using approximate curve factors2009Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 233, nr 4, s. 1117-1127Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Schwarz–Christoffel mapping from the upper half-plane to a polygonal region in the complex plane is an integral of a product with several factors, where each factor corresponds to a certain vertex in the polygon. Different modifications of the Schwarz–Christoffel mapping in which factors are replaced with the so-called curve factors to achieve polygons with rounded corners are known since long times. Among other requisites, the arguments of a curve factor and its correspondent scl factor must be equal outside some closed interval on the real axis.

    In this paper, the term approximate curve factor is defined such that many of the already known curve factors are included as special cases. Additionally, by alleviating the requisite on the argument from exact to asymptotic equality, new types of curve factors are introduced. While traditional curve factors have a C1 regularity, C regular approximate curve factors can be constructed, resulting in smooth boundary curves when used in conformal mappings.

    Applications include modelling of wave scattering in waveguides. When using approximate curve factors in modified Schwarz–Christoffel mappings, numerical conformal mappings can be constructed that preserve two important properties in the waveguides. First, the direction of the boundary curve can be well controlled, especially towards infinity, where the application requires two straight parallel walls. Second, a smooth (C) boundary curve can be achieved.

  • 5.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Numerical Conformal Mappings for Regions Bounded by Smooth Curves2006Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    In many applications, conformal mappings are used to transform twodimensional regions into simpler ones. One such region for which conformal mappings are needed is a channel bounded by continuously differentiable curves. In the applications that have motivated this work, it is important that the region an approximate conformal mapping produces, has this property, but also that the direction of the curve can be controlled, especially in the ends of the channel.

    This thesis treats three different methods for numerically constructing conformal mappings between the upper half–plane or unit circle and a region bounded by a continuously differentiable curve, where the direction of the curve in a number of control points is controlled, exact or approximately.

    The first method is built on an idea by Peter Henrici, where a modified Schwarz–Christoffel mapping maps the upper half–plane conformally on a polygon with rounded corners. His idea is used in an algorithm by which mappings for arbitrary regions, bounded by smooth curves are constructed.

    The second method uses the fact that a Schwarz–Christoffel mapping from the upper half–plane or unit circle to a polygon maps a region Q inside the half–plane or circle, for example a circle with radius less than 1 or a sector in the half–plane, on a region Ω inside the polygon bounded by a smooth curve. Given such a region Ω, we develop methods to find a suitable outer polygon and corresponding Schwarz–Christoffel mapping that gives a mapping from Q to Ω.

    Both these methods use the concept of tangent polygons to numerically determine the coefficients in the mappings.

    Finally, we use one of Don Marshall’s zipper algorithms to construct conformal mappings from the upper half–plane to channels bounded by arbitrary smooth curves, with the additional property that they are parallel straight lines when approaching infinity.

  • 6.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Numerical conformal mappings for waveguides2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with varying direction and cross-section can be re-formulated as a two-dimensional scattering problem, provided that the variations take place in only one dimension at a time. By using the so-called Building Block Method, it is possible to construct the scattering properties of a combination of scatterers when the properties of each scatterer are known. Hence, variations in the waveguide geometry or in the boundary conditions can be treated one at a time.

    Using the Building Block Method, the problem takes the form of the Helmholtz equation for stationary waves in a waveguide of infinite length and with smoothly varying geometry and boundary conditions. A conformal mapping is used to transform the problem into a corresponding problem in a straight horizontal waveguide, and by expanding the field in Fourier trigonometric series, the problem can be reformulated as an infinite-dimensional ordinary differential equation. From this, numerically solvable differential equations for the reflection and transmission operators are derived.

    To be applicable in the Building Block Method, the numerical conformal mapping must be constructed such that the direction of the boundary curve can be controlled. At the channel ends, it is an indispensable requirement, that the two boundary curves are (at least) asymptotically parallel and straight. Furthermore, to achieve bounded operators in the differential equations, the boundary curves must satisfy different regularity conditions, depending on the boundary conditions.

    In this work, several methods to accomplish such conformal mappings are presented. The Schwarz–Christoffel mapping, which is a natural starting point and for which also efficient numerical software exists, can be modified in different ways in order to achieve polygons with rounded corners. We present algorithms by which the parameters in the mappings can be determined after such modifications. We show also how the unmodified Schwarz–Christoffel mapping can be used for regions with a smooth boundary. This is done by constructing an appropriate outer polygon to the considered region.

    Finally, we introduce one method that is not Schwarz–Christoffel-related, by showing how one of the so-called zipper algorithms can be used for waveguides.

  • 7.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Numerical Conformal Mappings for Waveguides2010Inngår i: Computational Mathematics: Theory, Methods and Applications, Hauppauge NY, USA: Nova Science Publishers , 2010Kapittel i bok, del av antologi (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with  varying direction and cross-section can, if the variations takes  place in only one dimension at a time be re-formulated as a  two-dimensional scattering problem. By using the so-called  Building Block Method, it is possible to construct the  scattering properties of a combination of scatterers when the  properties of each scatterer are known. Hence, variations in the  waveguide geometry or in the boundary conditions can be treated   one at a time.  We consider in this work acoustic scattering, but the same  techniques can be used for both electro-magnetic and some quantum  scattering problems.  By suppressing the time dependence and by using the Building Block  Method, the problem takes the form of the Helmholtz equation in a  waveguide of infinite length and with smoothly varying geometry and  boundary conditions.  A conformal mapping is used to transform the  problem into a corresponding problem in a straight horizontal  channel, and by expanding the field in Fourier trigonometric series,  the problem can be reformulated as an infinite-dimensional ordinary  differential equation. From this, numerically solvable differential  equations for the reflection and transmission operators are  derived.  To be applicable in the Building Block Method, the numerical  conformal mapping must be constructed such that the direction of the  boundary curve can be controlled. At the channel ends, it is an  indispensable requirement, that the two boundary curves are (at least)  asymptotically parallel and straight. Furthermore, to achieve  bounded operators in the differential equations, the boundary curves  must satisfy different regularity conditions, depending on the  properties of the boundary.  Several methods to accomplish such conformal mappings are  presented. The Schwarz-Christoffel mapping, which is a natural starting point and for which  also efficient numerical software exists, can be modified in  different ways to round the polygon corners, and we show algorithms  by which the parameter problem can be solved after such  modifications. It is also possible to use the unmodified Schwarz-Christoffel mapping for  regions with smooth boundary, by constructing an appropriate outer  polygon to the considered region.  Finally, we show how a so-called  zipper algorithm can be used for waveguides.

  • 8.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    On the curvature of an inner curve in a Schwarz--Christoffel mapping2009Inngår i: Further Progress in Analysis: Proceedings of the 6th International ISAAC Congress, Ankara, Turkey, 2007, World Scientific , 2009, s. 281-290Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In the so called outer polygon method, an approximative conformal mapping for a given simply connected region Ω is constructed using a Schwarz–Christoffel mapping for an outer polygon, a polygonal region of which Ω is a subset. The resulting region is then bounded by a C-curve, which among other things means that its curvature is bounded.In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz–Christoffel mapping from R, the unit disk or upper half–plane, to a polygonal region P of a curve inside R. From the Schwarz–Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.

  • 9.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Schwarz-Christoffel Mappings for Nonpolygonal Regions2008Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, nr 1, s. 94-111Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An approximate conformal mapping for an arbitrary region Ω bounded by a smooth curve Γ is constructed using the Schwarz–Christoffel mapping for a polygonal region in which Ω is embedded. An algorithm for finding this so-called outer polygon is presented. The resulting function is a conformal mapping from the upper half-plane or the unit disk to a region R, approximately equal to Ω. R is bounded by a C∞ curve, and since the mapping function originates from the Schwarz–Christoffel mapping and tangent polygons are used to determine it, important properties of Γ such as direction, linear asymptotes, and inflexion points are preserved in the boundary of R. The method makes extensive use of existing Schwarz–Christoffel software in both the determination of outer polygons and the calculation of function values. By the use suggested here, the capabilities of such well-written software are extended.

  • 10.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Using a zipper algorithm to find a conformal map for a channel with smooth boundary2006Inngår i: Mathematical Modeling of Wave Phenomena: 2nd Conference, 2006, s. 378-Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The so called geodesic algorithm, which is one of the zipper algorithms for conformal mappings, is combined with a Schwarz–Christoffel mapping, in its original or in a modified form, to produce a conformal mapping function between the upper half-plane and an arbitrary channel with smooth boundary and parallel walls at the end.

  • 11.
    Andersson, Anders
    et al.
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Nilsson, Börje
    International Centre for Mathematical modelling, Växjö University.
    Acoustic Transmission in Ducts of Various Shapes with an Impedance Condition2008Inngår i: International Conference on Numerical Analysis and Applied Mathematics 2008, Melville: American Institute of Physics , 2008, s. 33-36Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Propagation of acoustic waves in a two-dimensional duct with an impedance condition at the boundary, is studied. The duct is assumed to have two ends at infinity being asymptotically straight, but otherwise to be arbitrarily shaped.The so called Building Block Method allows us to synthesize propagation properties for ducts with complicated geometries from results for simpler ducts. Conformal mappings can be used to transform these simple ducts to straight ducts with constant cross-sections.By using recently developed techniques for numerical conformal mappings, it is possible to construct a transformation between an infinite strip and an arbitrarily shaped duct with smooth or piecewise smooth boundary, keeping both smoothness and the well controlled boundary direction towards infinity that the above mentioned method requires.To accomplish a stable formulation of the problem, we express it in terms of scattering operators. The resulting differential equation is solved using wave splitting and invariant embedding techniques. We expand the involved functions in Fourier series, and hence, it is possible to give the operators a matrix representation. Numerical results are produced using truncated matrices.

  • 12.
    Andersson, Anders
    et al.
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Nilsson, Börje
    International Centre for Mathematical Modelling, Växjö University.
    Electro-Magnetic Scattering in Variously Shaped Waveguides with an Impedance Condition2009Inngår i: AIP Conference Proceedings: Third Conference on Mathematical Modeling of Wave Phenomena: Växjö, Sweden, 9-13 June, 2008, American Institute of Physics , 2009, s. 36-45Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Electro-magnetic scattering is studied in a waveguide with varying shape and crosssection. Furthermore, an impedance or admittance condition is applied to two of the waveguide walls. Under the condition that variations in geometry or impedance take place in only one plane at the time, the problem can be solved as a two-dimensional wave-scattering problems. By using newly developed numerical conformal mapping techniques, the problem is transformedinto a wave-scattering problem in a straight two-dimensional channel. A numerically stable formulation is reached in terms of transmission and reflection operators. Numerical results are given for a slowly varying waveguide with a bend and for one more complex geometry.

  • 13.
    Eckert, Gunnar
    et al.
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Hjelmåker, Monica
    Högskolan i Jönköping, Tekniska Högskolan.
    Elmquist, Lennart
    Högskolan i Jönköping, Tekniska Högskolan, JTH. Forskningsmiljö Material och tillverkning – Gjutning.
    Off campus integrating theory and practice with progression2013Konferansepaper (Annet vitenskapelig)
  • 14.
    Eklund, Peter
    et al.
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Haugthon, Johan
    JTH, Maskinteknik.
    Utveckling av universaladapter för torkblad i samarbete med European Automotive Supplier AB2007Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    This report looks at the possibility of designing a universal adapter for Flat Blade windshield wipers in cooperation with European Automotive Supplier AB.

    To understand and see if this is possible, a research and an extensive patent search where done. Then to add structure to the project a Ganttschematic were developed. To generate good and solid ideas, different methods for product development were looked upon.

    When a method was chosen and applied, a series of concepts emerged. Now the focus was to design and construct all the pieces. The desired manufacture procedures were looked upon as well as materials. Lot of time where spent on designing a lock mechanism to meet the demands European Automotive Supplier AB hade given. To choose the right concept the team used a set of selection matrix for the different ideas.

    After the choices were made, different prototypes were made of the concepts. Then they were tested, and improvement on them was done to make the end product better.

  • 15.
    Ivanov, Tjavdar
    et al.
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Maz'ya, Vladimir
    Schmidt, Gunther
    Boundary Layer Approximate Approximations and Cubature of Potentials in Domains1999Inngår i: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 10, nr 3-4, s. 311-342Artikkel i tidsskrift (Fagfellevurdert)
  • 16.
    Ivanov, Tjavdar
    et al.
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Maz'ya, Vladimir
    Schmidt, Gunther
    Boundary Layer Approximate Approximations for Cubature of Potentials2000Inngår i: Mathematical Aspects of Boundary Element Methods / [ed] M. Bonnet, A.-M. Sändig, W.L. Wendland, London: Chapman & Hall , 2000, s. 165-177Kapittel i bok, del av antologi (Annet vitenskapelig)
  • 17.
    Nilsson, Börje
    et al.
    International Centre of Mathematical Modelling, Växjö University, Sweden.
    Augey, Romain
    National Institute of Advanced Technology (ENSTA, Paris), France.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Acoustic waves in a mean flow duct with varying boundary2009Inngår i: 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), Reston, Va.: < American Institute of Aeronautics and Astronautics , 2009Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The problem of modelling sound waves in a two-dimensional wave-guide of general shape carrying a mean flow is addressed. The mean flowmay be inhomogeneous but is irrotational. A convective wave equation forthe velocity potential is derived. It is in a form suitable for generalizingan earlier developed theory for a stable modelling of acoustic waves inquiescent waveguides with complicated geometry to also include a meanflow. The theory is illustrated with numerical results for reflection andtransmission demonstrating the effectiveness of the method for low andmedium frequencies.

1 - 17 of 17
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