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1. A modiﬁed Schwarz-Christoffel mapping for regions with piecewise smooth boundaries Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt591",{id:"formSmash:items:resultList:0:j_idt591",widgetVar:"widget_formSmash_items_resultList_0_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A modiﬁed Schwarz-Christoffel mapping for regions with piecewise smooth boundaries2008In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 213, no 1, p. 56-70Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:0:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_0_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 2. Modified Schwarz-Christoffel mappings using approximate curve factors Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt591",{id:"formSmash:items:resultList:1:j_idt591",widgetVar:"widget_formSmash_items_resultList_1_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Modified Schwarz-Christoffel mappings using approximate curve factors2009In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 233, no 4, p. 1117-1127Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:1:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_1_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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

*C*^{1}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.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:1:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 3. Numerical Conformal Mappings for Regions Bounded by Smooth Curves Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt591",{id:"formSmash:items:resultList:2:j_idt591",widgetVar:"widget_formSmash_items_resultList_2_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Numerical Conformal Mappings for Regions Bounded by Smooth Curves2006Licentiate thesis, monograph (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:2:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_2_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:2:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 4. Numerical conformal mappings for waveguides Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt591",{id:"formSmash:items:resultList:3:j_idt591",widgetVar:"widget_formSmash_items_resultList_3_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Numerical conformal mappings for waveguides2009Doctoral thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:3:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_3_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:3:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 5. Numerical Conformal Mappings for Waveguides Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt591",{id:"formSmash:items:resultList:4:j_idt591",widgetVar:"widget_formSmash_items_resultList_4_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Numerical Conformal Mappings for Waveguides2010In: Computational Mathematics: Theory, Methods and Applications, Hauppauge NY, USA: Nova Science Publishers , 2010Chapter in book (Other (popular science, discussion, etc.))Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:4:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_4_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:4:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 6. On the curvature of an inner curve in a Schwarz--Christoffel mapping Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt591",{id:"formSmash:items:resultList:5:j_idt591",widgetVar:"widget_formSmash_items_resultList_5_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On the curvature of an inner curve in a Schwarz--Christoffel mapping2009In: Further Progress in Analysis: Proceedings of the 6th International ISAAC Congress, Ankara, Turkey, 2007, World Scientific , 2009, p. 281-290Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:5:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_5_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:5:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 7. Schwarz-Christoffel Mappings for Nonpolygonal Regions Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt591",{id:"formSmash:items:resultList:6:j_idt591",widgetVar:"widget_formSmash_items_resultList_6_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Schwarz-Christoffel Mappings for Nonpolygonal Regions2008In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, no 1, p. 94-111Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:6:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_6_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:6:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 8. Using a zipper algorithm to find a conformal map for a channel with smooth boundary Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt591",{id:"formSmash:items:resultList:7:j_idt591",widgetVar:"widget_formSmash_items_resultList_7_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Using a zipper algorithm to find a conformal map for a channel with smooth boundary2006In: Mathematical Modeling of Wave Phenomena: 2nd Conference, 2006, p. 378-Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:7:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_7_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 9. Acoustic Transmission in Ducts of Various Shapes with an Impedance Condition Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt591",{id:"formSmash:items:resultList:8:j_idt591",widgetVar:"widget_formSmash_items_resultList_8_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt594",{id:"formSmash:items:resultList:8:j_idt594",widgetVar:"widget_formSmash_items_resultList_8_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Nilsson, BörjeInternational Centre for Mathematical modelling, Växjö University.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Acoustic Transmission in Ducts of Various Shapes with an Impedance Condition2008In: International Conference on Numerical Analysis and Applied Mathematics 2008, Melville: American Institute of Physics , 2008, p. 33-36Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:8:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_8_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. Electro-Magnetic Scattering in Variously Shaped Waveguides with an Impedance Condition Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt591",{id:"formSmash:items:resultList:9:j_idt591",widgetVar:"widget_formSmash_items_resultList_9_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt594",{id:"formSmash:items:resultList:9:j_idt594",widgetVar:"widget_formSmash_items_resultList_9_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Nilsson, BörjeInternational Centre for Mathematical Modelling, Växjö University.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Electro-Magnetic Scattering in Variously Shaped Waveguides with an Impedance Condition2009In: AIP Conference Proceedings: Third Conference on Mathematical Modeling of Wave Phenomena: Växjö, Sweden, 9-13 June, 2008, American Institute of Physics , 2009, p. 36-45Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:9:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_9_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Fourier methods for harmonic scalar waves in general waveguides Andersson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt591",{id:"formSmash:items:resultList:10:j_idt591",widgetVar:"widget_formSmash_items_resultList_10_j_idt591",onLabel:"Andersson, Anders ",offLabel:"Andersson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt594",{id:"formSmash:items:resultList:10:j_idt594",widgetVar:"widget_formSmash_items_resultList_10_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Nilsson, BörjeLinnaeus university, Vaxjö, Sweden.Biro, ThomasJönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fourier methods for harmonic scalar waves in general waveguides2016In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 98, no 1, p. 21-38Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:10:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_10_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A set of semi-analytic techniques based on Fourier analysis is used to solve wave-scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are the newly developed conformal mapping methods, wave splitting, Fourier series expansions in eigenfunctions to non-normal operators, the building block method or the cascade technique, Dirichlet-to-Neumann operators, and reformulation in terms of stable differential equations for reflection and transmission matrices. For an example, the results show good correspondence with a finite element method solution to the same problem in the low- and medium-frequency domains. The Fourier method complements finite element analysis as a waveguide simulation tool. For inverse engineering involving tuning of straight waveguide parts joining complicated waveguide elements, the Fourier method is an attractive alternative including time aspects. The prime motivation for the Fourier method is its added physical understanding primarily at low frequencies.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:10:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 12. Acoustic waves in a mean flow duct with varying boundary Nilsson, Börje PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt591",{id:"formSmash:items:resultList:11:j_idt591",widgetVar:"widget_formSmash_items_resultList_11_j_idt591",onLabel:"Nilsson, Börje ",offLabel:"Nilsson, Börje ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt594",{id:"formSmash:items:resultList:11:j_idt594",widgetVar:"widget_formSmash_items_resultList_11_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); International Centre of Mathematical Modelling, Växjö University, Sweden.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Augey, RomainNational Institute of Advanced Technology (ENSTA, Paris), France.Andersson, AndersJönköping University, School of Engineering, JTH, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Acoustic waves in a mean flow duct with varying boundary2009In: 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), Reston, Va.: < American Institute of Aeronautics and Astronautics , 2009Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:11:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_11_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); 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.

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