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Lehto, Erik

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### von Sydow, Lina

### Ghafari, Paria

### Lehto, Erik

### Wångersjö, Mats

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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
#####

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##### Projects

eSSENCE
Available from: 2016-11-11 Created: 2016-12-02 Last updated: 2017-05-04Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Open this publication in new window or tab >>A scalable RBF–FD method for atmospheric flow### Tillenius, Martin

### Larsson, Elisabeth

### Lehto, Erik

### Flyer, Natasha

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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 ()
#####

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##### Projects

eSSENCEUPMARC
Available from: 2015-06-15 Created: 2015-06-24 Last updated: 2018-01-11Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

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### Tillenius, Martin

### Larsson, Elisabeth

### Lehto, Erik

### Flyer, Natasha

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##### 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)
#####

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##### Projects

eSSENCEUPMARC
Available from: 2014-04-03 Created: 2014-03-25 Last updated: 2018-01-11Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Open this publication in new window or tab >>A task parallel implementation of a scattered node stencil-based solver for the shallow water equations### Tillenius, Martin

### Larsson, Elisabeth

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.### Lehto, Erik

### Flyer, Natasha

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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
#####

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##### Projects

eSSENCEUPMARC
Available from: 2013-11-25 Created: 2013-11-27 Last updated: 2018-01-11Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.

Open this publication in new window or tab >>Stable calculation of Gaussian-based RBF-FD stencils### Fornberg, Bengt

### Lehto, Erik

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Powell, Collin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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 ()
#####

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Available from: 2012-12-08 Created: 2013-02-13 Last updated: 2017-12-06Bibliographically approved

Open this publication in new window or tab >>Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions### Larsson, Elisabeth

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Lehto, Erik

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Heryudono, Alfa

### Fornberg, Bengt

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 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 ()
#####

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Available from: 2013-08-22 Created: 2013-08-26 Last updated: 2017-12-06Bibliographically approved

Open this publication in new window or tab >>A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere### Flyer, Natasha

### Lehto, Erik

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Blaise, Sébastien

### Wright, Grady B.

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##### National Category

Computational Mathematics Computer Sciences
##### Identifiers

urn:nbn:se:uu:diva-173564 (URN)10.1016/j.jcp.2012.01.028 (DOI)000302933600004 ()
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Available from: 2012-02-16 Created: 2012-04-26 Last updated: 2018-01-12Bibliographically approved

Open this publication in new window or tab >>High Order Local Radial Basis Function Methods for Atmospheric Flow Simulations### Lehto, Erik

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2012 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### 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

### Driscoll, Tobin

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##### Supervisors

### Larsson, Elisabeth

### Flyer, Natasha

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Available from: 2012-08-29 Created: 2012-08-09 Last updated: 2013-01-22Bibliographically approved

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.

University of Delaware, Department of Mathematical Sciences.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.

National Center for Atmospheric Research, Institute for Mathematics Applied to Geosciences.

Open this publication in new window or tab >>Stable calculation of Gaussian-based RBF-FD stencils### Fornberg, Bengt

### Lehto, Erik

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Powell, Collin

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##### 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)
#####

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Available from: 2012-08-09 Created: 2012-08-09 Last updated: 2012-09-12Bibliographically approved

Open this publication in new window or tab >>Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions### Larsson, Elisabeth

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Lehto, Erik

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.### Heryudono, Alfa

### Fornberg, Bengt

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 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)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt359",{id:"formSmash:j_idt184:9:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt359",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt365",{id:"formSmash:j_idt184:9:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt365",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt371",{id:"formSmash:j_idt184:9:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt371",multiple:true});
#####

Available from: 2012-08-13 Created: 2012-08-09 Last updated: 2012-09-12Bibliographically approved