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Kjellmert, Bo
Publications (10 of 12) Show all publications
Kjellmert, B. (2016). Electromagnetic eigenfields in checkerboard patterns (ed.). Paper presented at . Numerical Methods for Partial Differential Equations, 32(2), 418-444
Open this publication in new window or tab >>Electromagnetic eigenfields in checkerboard patterns
2016 (English)In: Numerical Methods for Partial Differential Equations, ISSN 0749-159X, E-ISSN 1098-2426, Vol. 32, no 2, p. 418-444Article in journal (Refereed) Published
Abstract [en]

Here are described four solvers for time-harmonic electromagnetic fields in checkerboard patterns. A pattern is built by four squares with constant permittivity, inline image or inline image. It is enclosed by conducting walls or is a unit cell of a periodic structure. The field is represented in two ways: by inline image, the transverse component of the magnetic induction, and by inline image, the magnetic vector potential in Lorenz gauge. inline image and inline image satisfy Helmholtz equations in each square as well as transmission and boundary conditions (BCs). These governing equations yield eigensolutions inline image and inline image, which are found to be inline image at worst. Variational versions of the governing equations are introduced. The weak formulations for inline image are standard, while those for inline image are new. They imply that the derivative transmission and BCs are satisfied weakly on interfaces between regions with different permittivity. Eigenpairs are computed approximately by spectral element methods. They yield mutually consistent eigenpairs. However, only about half of the eigenpairs (inline image) correspond to eigenpairs (inline image). For each set of BCs, the first few eigenfrequencies inline image are given by tables, and some of the eigenfunctions are presented by contour plots.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-13509 (URN)10.1002/num.22000 (DOI)000369535400003 ()2-s2.0-84956752638 (Scopus ID)cbc3356e-dc00-44d7-9f2b-2991c58c8778 (Local ID)cbc3356e-dc00-44d7-9f2b-2991c58c8778 (Archive number)cbc3356e-dc00-44d7-9f2b-2991c58c8778 (OAI)
Note
Validerad; 2016; Nivå 2; 20150826 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kjellmert, B. (2014). A numerical study of electromagnetic waves in periodic waveguides (ed.). Paper presented at . Numerical Methods for Partial Differential Equations, 30(2), 490-513
Open this publication in new window or tab >>A numerical study of electromagnetic waves in periodic waveguides
2014 (English)In: Numerical Methods for Partial Differential Equations, ISSN 0749-159X, E-ISSN 1098-2426, Vol. 30, no 2, p. 490-513Article in journal (Refereed) Published
Abstract [en]

Here are considered time-harmonic electromagnetic waves in a quadratic waveguide consisting of a periodic dielectric core enclosed by conducting walls. The permittivity function may be smooth or have jumps. The electromagnetic field is given by a magnetic vector potential in Lorenz gauge, and defined on a Floquet cell. The Helmholtz operator is approximated by a Chebyshev collocation, Fourier–Galerkin method. Laurent's rule and the inverse rule are employed for the representation of Fourier coefficients of products of functions. The computations yield, for known wavenumbers, values of the first few eigenfrequencies of the field. In general, the dispersion curves exhibit band gaps. Field patterns are identified as transverse electric, TE, transverse magnetic, TM, or hybrid modes. Maxwell's equations are fulfilled. A few trivial solutions appear when the permittivity varies in the guiding direction and across it. The results of the present method are consistent with exact results and with those obtained by a low-order finite element software. The present method is more efficient than the low-order finite element method

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-14978 (URN)10.1002/num.21821 (DOI)2-s2.0-84893691309 (Scopus ID)e6f480fe-58b5-4fd2-928e-b5070e7fc32a (Local ID)e6f480fe-58b5-4fd2-928e-b5070e7fc32a (Archive number)e6f480fe-58b5-4fd2-928e-b5070e7fc32a (OAI)
Note
Validerad; 2014; 20131105 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kjellmert, B. & Strömberg, T. (2009). Time-dependent electromagnetic waves in a cavity (ed.). Paper presented at . Applications of Mathematics, 54(1), 17-45
Open this publication in new window or tab >>Time-dependent electromagnetic waves in a cavity
2009 (English)In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 54, no 1, p. 17-45Article in journal (Refereed) Published
Abstract [en]

The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential A satisfying a wave equation with initial-boundary conditions. This description through A is rigorously shown to give a unique solution of the problem and is the starting point for numerical computations. A Chebyshev collocation solver has been implemented for a cubic cavity, and it has been compared to a standard finite element solver. The results obtained are consistent while the collocation solver performs substantially faster. Some time histories and spectra are computed.

National Category
Mathematical Analysis Computational Mathematics
Research subject
Mathematics; Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-7500 (URN)10.1007/s10492-009-0002-z (DOI)000263057800002 ()2-s2.0-84867982746 (Scopus ID)5e55c950-6b48-11dc-9e58-000ea68e967b (Local ID)5e55c950-6b48-11dc-9e58-000ea68e967b (Archive number)5e55c950-6b48-11dc-9e58-000ea68e967b (OAI)
Note
Validerad; 2009; 20070925 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kjellmert, B. (1999). A spectral method to solve the equations of linear elasticity for the transient response of a tube subjected to impact (ed.). Paper presented at . International Journal for Numerical Methods in Engineering, 45(8), 1115-1133
Open this publication in new window or tab >>A spectral method to solve the equations of linear elasticity for the transient response of a tube subjected to impact
1999 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 45, no 8, p. 1115-1133Article in journal (Refereed) Published
Abstract [en]

The transient response of a tube subjected to impact is described through Fourier-Galerkin and Chebyshev collocation multidomain discretizations of the equations of linear elasticity. The trapezoidal rule is used for time integration. For each Fourier mode the spatial collocation derivative operators are represented by matrices, and the subdomains are patched by natural and essential conditions. At each time level the resulting governing matrix equation is reduced by two consecutive block Gaussian eliminations, so that an equation for the complex Fourier coefficients at die subdomain corners has to be solved. Back-substitution gives the coefficients at all other collocation points. An inverse discrete Fourier transform generates, at optional time levels, the three components of the displacement field. Through this method the long-term evolution of the field may be calculated, provided the impact time is long enough. The time history as represented by computed contour plots has been compared with photos produced by holographic interferometry. The agreements are satisfactory.

National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-13365 (URN)10.1002/(SICI)1097-0207(19990720)45:83.0.CO;2-J (DOI)c9451a50-ee91-11dc-a549-000ea68e967b (Local ID)c9451a50-ee91-11dc-a549-000ea68e967b (Archive number)c9451a50-ee91-11dc-a549-000ea68e967b (OAI)
Note
Godkänd; 1999; 20080310 (cira)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Kjellmert, B. (1997). A Chebyshev collocation multidomain method to solve the Reissner-Mindlin equations for the transient response of an anisotropic plate subjected to impact (ed.). Paper presented at . International Journal for Numerical Methods in Engineering, 40(20), 3689-3702
Open this publication in new window or tab >>A Chebyshev collocation multidomain method to solve the Reissner-Mindlin equations for the transient response of an anisotropic plate subjected to impact
1997 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 40, no 20, p. 3689-3702Article in journal (Refereed) Published
Abstract [en]

The transient response of an anisotropic rectangular plate subjected to impact is described through a Chebyshev collocation multidomain discretization of the Reissner-Mindlin plate equations. The trapezoidal rule is used for time-integration. The spatial collocation derivative operators are represented by matrices, and the subdomains are patched by natural and essential conditions. At each time level the resulting governing matrix equation is reduced by two consecutive block Gaussian eliminations, so that an equation for the variables at the subdomain corners has to be solved. Back-substitution gives the variables at all other collocation points. The time history as represented by computed contour plots has been compared with analytical results and with photos produced by holographic interferometry. The agreements are satisfactory

National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-13979 (URN)10.1002/(SICI)1097-0207(19971030)40:203.0.CO;2-E (DOI)d4e764c0-6f89-11dd-8151-000ea68e967b (Local ID)d4e764c0-6f89-11dd-8151-000ea68e967b (Archive number)d4e764c0-6f89-11dd-8151-000ea68e967b (OAI)
Note
Godkänd; 1997; 20080821 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Bucht, T., Kjellmert, B. & Löfqvist, T. (1995). Experimentell metodik (5ed.). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Experimentell metodik
1995 (Swedish)Book (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 1995 Edition: 5
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering Computational Mathematics
Research subject
Industrial Electronics; Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-16754 (URN)e93e8b90-bec4-11dc-b185-000ea68e967b (Local ID)e93e8b90-bec4-11dc-b185-000ea68e967b (Archive number)e93e8b90-bec4-11dc-b185-000ea68e967b (OAI)
Note
Godkänd; 1995; 20080109 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Kjellmert, B. (1991). Comparative study of the behaviour of a direct solver and a preconditioned iterative solver for the equations arising from the discretization by Chebyshev collocation of a second-order partial differential equation on a square (ed.). Paper presented at . International Journal for Numerical Methods in Engineering, 32(1), 527-539
Open this publication in new window or tab >>Comparative study of the behaviour of a direct solver and a preconditioned iterative solver for the equations arising from the discretization by Chebyshev collocation of a second-order partial differential equation on a square
1991 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 32, no 1, p. 527-539Article in journal (Refereed) Published
Abstract [en]

The behaviour is compared of two solvers for the discrete equations arising from the discretization using Chebyshev collocation of a second-order linear partial differential equation on a square. The alternative solvers considered are a direct solver and an iterative solver based on preconditioning with the matrix arising from finite-difference discretization of the governing equation. The total error of the collocation derivatives and the separate contributions from round-off and discretization error are examined. The efficiency of the two solvers is compared. The iterative solver is more efficient than the direct solver on fine grids for equations similar to the Poisson equation, provided that there are Dirichlet boundary conditions on at least three of the sides of the square.

National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-8889 (URN)10.1002/nme.1620320305 (DOI)A1991GD24800004 ()2-s2.0-0026205397 (Scopus ID)770bb990-6f8a-11dd-8151-000ea68e967b (Local ID)770bb990-6f8a-11dd-8151-000ea68e967b (Archive number)770bb990-6f8a-11dd-8151-000ea68e967b (OAI)
Note
Godkänd; 1991; 20080821 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kjellmert, B. (1991). Multidomain collocation techniques for a viscous compressible flow (ed.). Paper presented at . International Journal for Numerical Methods in Fluids, 13(5), 643-653
Open this publication in new window or tab >>Multidomain collocation techniques for a viscous compressible flow
1991 (English)In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 13, no 5, p. 643-653Article in journal (Refereed) Published
Abstract [en]

This paper presents a viscous compressible flow problem to which an equilibrium solution, in terms of density and velocity, can be given implicitly by elementary functions. The corresponding initial boundary value problem is solved by time discretization by the Crank-Nicolson method, Newton linearization and space discretization using multidomain Chebyshev collocation techniques. The physical interval is covered by subintervals of equal length. Each subinterval utilizes the same number of collocation points and each interface consists of one or two points. Six ways of patching are tested. All of them yield solutions with spectral accuracy for a few time steps, but only three are stable in the long run. Details of the density evolution are illustrated

National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-3940 (URN)10.1002/fld.1650130507 (DOI)A1991GE98600006 ()2-s2.0-0026417174 (Scopus ID)1c9c1fc0-065a-11dd-97e0-000ea68e967b (Local ID)1c9c1fc0-065a-11dd-97e0-000ea68e967b (Archive number)1c9c1fc0-065a-11dd-97e0-000ea68e967b (OAI)
Note
Godkänd; 1991; 20080409 (cira)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kjellmert, B. (1988). Chebyshev pseudospectral solution of a one-dimensional flow problem: numerical experiments (ed.). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Chebyshev pseudospectral solution of a one-dimensional flow problem: numerical experiments
1988 (English)Report (Other academic)
Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 1988
Series
Research report / Luleå University of Technology1 jan 1974 → 31 dec 1996, ISSN 0347-0881 ; 1988:17
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-23630 (URN)7c279ab0-bec4-11dc-b185-000ea68e967b (Local ID)7c279ab0-bec4-11dc-b185-000ea68e967b (Archive number)7c279ab0-bec4-11dc-b185-000ea68e967b (OAI)
Note
Godkänd; 1988; 20080109 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Kjellmert, B. & Lindfors, C. (1983). Konvektion i ventilerade lådor: strömningsbilder och temperaturfördelningar (ed.). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Konvektion i ventilerade lådor: strömningsbilder och temperaturfördelningar
1983 (Swedish)Report (Other academic)
Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 1983
Series
Technical report / Luleå University of Technology… → 31 dec 1996, ISSN 0349-3571 ; 1983:64
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-22985 (URN)5254dbc0-bec5-11dc-b185-000ea68e967b (Local ID)5254dbc0-bec5-11dc-b185-000ea68e967b (Archive number)5254dbc0-bec5-11dc-b185-000ea68e967b (OAI)
Note
Godkänd; 1983; 20080109 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
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