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Lehto, Erik
Publications (10 of 13) Show all publications
von Sydow, L., Ghafari, P., Lehto, E. & Wångersjö, M. (2016). Pricing of basket options using dimension reduction and adaptive finite differences in space, and discontinuous Galerkin in time. In: Numerical Mathematics and Advanced Applications: ENUMATH 2015. Paper presented at ENUMATH 2015 (pp. 607-615). Springer
Open this publication in new window or tab >>Pricing of basket options using dimension reduction and adaptive finite differences in space, and discontinuous Galerkin in time
2016 (English)In: Numerical Mathematics and Advanced Applications: ENUMATH 2015, Springer, 2016, p. 607-615Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Springer, 2016
Series
Lecture Notes in Computational Science and Engineering ; 112
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-309279 (URN)10.1007/978-3-319-39929-4_58 (DOI)000398020000058 ()978-3-319-39927-0 (ISBN)
Conference
ENUMATH 2015
Projects
eSSENCE
Available from: 2016-11-11 Created: 2016-12-02 Last updated: 2017-05-04Bibliographically approved
Tillenius, M., Larsson, E., Lehto, E. & Flyer, N. (2015). A scalable RBF–FD method for atmospheric flow. Journal of Computational Physics, 298, 406-422
Open this publication in new window or tab >>A scalable RBF–FD method for atmospheric flow
2015 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 298, p. 406-422Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-256651 (URN)10.1016/j.jcp.2015.06.003 (DOI)000358796700023 ()
Projects
eSSENCEUPMARC
Available from: 2015-06-15 Created: 2015-06-24 Last updated: 2018-01-11Bibliographically approved
Tillenius, M., Larsson, E., Lehto, E. & Flyer, N. (2014). A task parallel implementation of an RBF-generated finite difference method for the shallow water equations on the sphere.
Open this publication in new window or tab >>A task parallel implementation of an RBF-generated finite difference method for the shallow water equations on the sphere
2014 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2014-011
National Category
Computer Sciences Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-221156 (URN)
Projects
eSSENCEUPMARC
Available from: 2014-04-03 Created: 2014-03-25 Last updated: 2018-01-11Bibliographically approved
Tillenius, M., Larsson, E., Lehto, E. & Flyer, N. (2013). A task parallel implementation of a scattered node stencil-based solver for the shallow water equations. In: Proc. 6th Swedish Workshop on Multi-Core Computing: . Paper presented at MCC13 (pp. 33-36). Halmstad, Sweden: Halmstad University
Open this publication in new window or tab >>A task parallel implementation of a scattered node stencil-based solver for the shallow water equations
2013 (English)In: Proc. 6th Swedish Workshop on Multi-Core Computing, Halmstad, Sweden: Halmstad University , 2013, p. 33-36Conference paper, Published paper (Other academic)
Place, publisher, year, edition, pages
Halmstad, Sweden: Halmstad University, 2013
National Category
Software Engineering
Identifiers
urn:nbn:se:uu:diva-211662 (URN)
Conference
MCC13
Projects
eSSENCEUPMARC
Available from: 2013-11-25 Created: 2013-11-27 Last updated: 2018-01-11Bibliographically approved
Fornberg, B., Lehto, E. & Powell, C. (2013). Stable calculation of Gaussian-based RBF-FD stencils. Computers and Mathematics with Applications, 65, 627-637
Open this publication in new window or tab >>Stable calculation of Gaussian-based RBF-FD stencils
2013 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 65, p. 627-637Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-194424 (URN)10.1016/j.camwa.2012.11.006 (DOI)000315425100006 ()
Available from: 2012-12-08 Created: 2013-02-13 Last updated: 2017-12-06Bibliographically approved
Larsson, E., Lehto, E., Heryudono, A. & Fornberg, B. (2013). Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions. SIAM Journal on Scientific Computing, 35, A2096-A2119
Open this publication in new window or tab >>Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions
2013 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 35, p. A2096-A2119Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-206046 (URN)10.1137/120899108 (DOI)000323892500014 ()
Available from: 2013-08-22 Created: 2013-08-26 Last updated: 2017-12-06Bibliographically approved
Flyer, N., Lehto, E., Blaise, S., Wright, G. B. & St-Cyr, A. (2012). A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere. Journal of Computational Physics, 231, 4078-4095
Open this publication in new window or tab >>A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere
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2012 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, p. 4078-4095Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-173564 (URN)10.1016/j.jcp.2012.01.028 (DOI)000302933600004 ()
Available from: 2012-02-16 Created: 2012-04-26 Last updated: 2018-01-12Bibliographically approved
Lehto, E. (2012). High Order Local Radial Basis Function Methods for Atmospheric Flow Simulations. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
Open this publication in new window or tab >>High Order Local Radial Basis Function Methods for Atmospheric Flow Simulations
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Since the introduction of modern computers, numerical methods for atmospheric simulations have routinely been applied for weather prediction, and in the last fifty years, there has been a steady improvement in the accuracy of forecasts. Accurate numerical models of the atmosphere are also becoming more important as researchers rely on global climate simulations to assess and understand the impact of global warming.

The choice of grid in a numerical model is an important design decision and no obvious optimal choice exists for computations in spherical geometry. Despite this disadvantage, grid-based methods are found in all current circulation models. A different approach to the issue of discretizing the surface of the sphere is given by meshless methods, of which radial basis function (RBF) methods are becoming prevalent.

In this thesis, RBF methods for simulation of atmospheric flows are explored. Several techniques are introduced to increase the efficiency of the methods. By utilizing a novel algorithm for adaptively placing the node points, accuracy is shown to improve by over one order of magnitude for two relevant test problems. The computational cost can also be reduced by using a local finite difference-like RBF scheme. However, this requires a stabilization mechanism for the hyperbolic problems of interest here. A hyper-viscosity scheme is introduced to address this issue.

Another stability issue arising from the ill-conditioning of the RBF basis for almost-flat basis functions is also discussed in the thesis, and two algorithms are proposed for dealing with this stability problem. The algorithms are specifically tailored for the task of creating finite difference weights using RBFs and are expected to overcome the issue of stationary error in local RBF collocation.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. p. 37
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 951
Keywords
Radial basis function, meshless method, high order finite difference, atmospheric flow, hyper-viscosity, stable algorithm
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-179194 (URN)978-91-554-8421-7 (ISBN)
Public defence
2012-09-21, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2012-08-29 Created: 2012-08-09 Last updated: 2013-01-22Bibliographically approved
Fornberg, B., Lehto, E. & Powell, C. (2012). Stable calculation of Gaussian-based RBF-FD stencils.
Open this publication in new window or tab >>Stable calculation of Gaussian-based RBF-FD stencils
2012 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-018
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-179192 (URN)
Available from: 2012-08-09 Created: 2012-08-09 Last updated: 2012-09-12Bibliographically approved
Larsson, E., Lehto, E., Heryudono, A. & Fornberg, B. (2012). Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions.
Open this publication in new window or tab >>Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions
2012 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-020
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-179191 (URN)
Available from: 2012-08-13 Created: 2012-08-09 Last updated: 2012-09-12Bibliographically approved
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