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af Klinteberg, LudvigORCID iD iconorcid.org/0000-0001-7425-8029
Publications (10 of 14) Show all publications
Fryklund, F., af Klinteberg, L. & Tornberg, A.-K. (2022). An adaptive kernel-split quadrature method for parameter-dependent layer potentials. Advances in Computational Mathematics, 48(2), Article ID 12.
Open this publication in new window or tab >>An adaptive kernel-split quadrature method for parameter-dependent layer potentials
2022 (English)In: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 48, no 2, article id 12Article in journal (Refereed) Published
Abstract [en]

Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer potentials belonging to the modified Helmholtz, modified biharmonic, and modified Stokes equations. These equations depend on a parameter, denoted alpha, and kernel-split quadrature loses its accuracy rapidly when this parameter grows beyond a certain threshold. This paper describes an algorithm that remedies this problem, using per-target adaptive sampling of the source geometry. The refinement is carried out through recursive bisection, with a carefully selected rule set. This maintains accuracy for a wide range of the parameter alpha, at an increased cost that scales as log alpha. Using this algorithm allows kernel-split quadrature to be both accurate and efficient for a much wider range of problems than previously possible.

Place, publisher, year, edition, pages
Springer Nature, 2022
Keywords
Integral equations, Partial differential equations, Layer potentials, Modified Helmholtz equation, Modified Stokes equation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-310254 (URN)10.1007/s10444-022-09927-5 (DOI)000766563600001 ()2-s2.0-85126240977 (Scopus ID)
Note

QC 20220325

Available from: 2022-03-25 Created: 2022-03-25 Last updated: 2022-06-25Bibliographically approved
af Klinteberg, L., Sorgentone, C. & Tornberg, A.-K. (2022). Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions. Computers and Mathematics with Applications, 111, 1-19
Open this publication in new window or tab >>Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions
2022 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 111, p. 1-19Article in journal (Refereed) Published
Abstract [en]

The quadrature error associated with a regular quadrature rule for evaluation of a layer potential increases rapidly when the evaluation point approaches the surface and the integral becomes nearly singular. Error estimates are needed to determine when the accuracy is insufficient and a more costly special quadrature method should be utilized.& nbsp;The final result of this paper are such quadrature error estimates for the composite Gauss-Legendre rule and the global trapezoidal rule, when applied to evaluate layer potentials defined over smooth curved surfaces in R-3. The estimates have no unknown coefficients and can be efficiently evaluated given the discretization of the surface, invoking a local one-dimensional root-finding procedure. They are derived starting with integrals over curves, using complex analysis involving contour integrals, residue calculus and branch cuts. By complexifying the parameter plane, the theory can be used to derive estimates also for curves in R3. These results are then used in the derivation of the estimates for integrals over surfaces. In this procedure, we also obtain error estimates for layer potentials evaluated over curves in R2. Such estimates combined with a local root-finding procedure for their evaluation were earlier derived for the composite Gauss-Legendre rule for layer potentials written in complex form [4]. This is here extended to provide quadrature error estimates for both complex and real formulations of layer potentials, both for the Gauss-Legendre and the trapezoidal rule.& nbsp;Numerical examples are given to illustrate the performance of the quadrature error estimates. The estimates for integration over curves are in many cases remarkably precise, and the estimates for curved surfaces in R-3 are also sufficiently precise, with sufficiently low computational cost, to be practically useful.

Place, publisher, year, edition, pages
Elsevier BV, 2022
Keywords
Layer potential, Close evaluation, Quadrature, Nearly singular, Error estimate
National Category
Atom and Molecular Physics and Optics Applied Mechanics Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-312763 (URN)10.1016/j.camwa.2022.02.001 (DOI)000789919800001 ()2-s2.0-85124958447 (Scopus ID)
Note

QC 20220523

Available from: 2022-05-23 Created: 2022-05-23 Last updated: 2022-06-25Bibliographically approved
af Klinteberg, L. & Tornberg, A.-K. (2018). Adaptive Quadrature by Expansion for Layer Potential Evaluation in Two Dimensions. SIAM Journal on Scientific Computing, 40(3), A1225-A1249
Open this publication in new window or tab >>Adaptive Quadrature by Expansion for Layer Potential Evaluation in Two Dimensions
2018 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 40, no 3, p. A1225-A1249Article in journal (Refereed) Published
Abstract [en]

When solving partial differential equations using boundary integral equation methods, accurate evaluation of singular and nearly singular integrals in layer potentials is crucial. A recent scheme for this is quadrature by expansion (QBX), which solves the problem by locally approximating the potential using a local expansion centered at some distance from the source boundary. In this paper we introduce an extension of the QBX scheme in two dimensions (2D) denoted AQBX—adaptive quadrature by expansion—which combines QBX with an algorithm for automated selection of parameters, based on a target error tolerance. A key component in this algorithm is the ability to accurately estimate the numerical errors in the coefficients of the expansion. Combining previous results for flat panels with a procedure for taking the panel shape into account, we derive such error estimates for arbitrarily shaped boundaries in 2D that are discretized using panel-based Gauss–Legendre quadrature. Applying our scheme to numerical solutions of Dirichlet problems for the Laplace and Helmholtz equations, and also for solving these equations, we find that the scheme is able to satisfy a given target tolerance to within an order of magnitude, making it useful for practical applications. This represents a significant simplification over the original QBX algorithm, in which choosing a good set of parameters can be hard.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2018
Keywords
boundary integral equation, adaptive, quadrature, nearly singular, error estimate
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-227312 (URN)10.1137/17M1121615 (DOI)000436986000021 ()2-s2.0-85044166523 (Scopus ID)
Funder
Göran Gustafsson Foundation for Research in Natural Sciences and MedicineSwedish Research Council, 2015-04998
Note

QC 20180508

Available from: 2018-05-07 Created: 2018-05-07 Last updated: 2024-03-18Bibliographically approved
af Klinteberg, L. & Tornberg, A.-K. (2017). Error estimation for quadrature by expansion in layer potential evaluation. Advances in Computational Mathematics, 43(1), 195-234
Open this publication in new window or tab >>Error estimation for quadrature by expansion in layer potential evaluation
2017 (English)In: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 43, no 1, p. 195-234Article in journal (Refereed) Published
Abstract [en]

In boundary integral methods it is often necessary to evaluate layer potentials on or close to the boundary, where the underlying integral is difficult to evaluate numerically. Quadrature by expansion (QBX) is a new method for dealing with such integrals, and it is based on forming a local expansion of the layer potential close to the boundary. In doing so, one introduces a new quadrature error due to nearly singular integration in the evaluation of expansion coefficients. Using a method based on contour integration and calculus of residues, the quadrature error of nearly singular integrals can be accurately estimated. This makes it possible to derive accurate estimates for the quadrature errors related to QBX, when applied to layer potentials in two and three dimensions. As examples we derive estimates for the Laplace and Helmholtz single layer potentials. These results can be used for parameter selection in practical applications.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Error estimate, Layer potential, Nearly singular, Quadrature
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-201960 (URN)10.1007/s10444-016-9484-x (DOI)000392330500010 ()2-s2.0-84991109241 (Scopus ID)
Funder
Göran Gustafsson Foundation for Research in Natural Sciences and MedicineSwedish Research Council, 2011-3178
Note

QC 20170303

Available from: 2017-03-03 Created: 2017-03-03 Last updated: 2022-10-24Bibliographically approved
af Klinteberg, L., Saffar Shamshirgar, D. & Tornberg, A.-K. (2017). Fast Ewald summation for free-space Stokes potentials. Research in the Mathematical Sciences, 4(1)
Open this publication in new window or tab >>Fast Ewald summation for free-space Stokes potentials
2017 (English)In: Research in the Mathematical Sciences, ISSN 2197-9847, Vol. 4, no 1Article in journal (Refereed) Published
Abstract [en]

We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, stresslets and rotlets that appear in boundary integral methods and potential methods for solving Stokes equations. The method combines the framework of the Spectral Ewald method for periodic problems (Lindbo and Tornberg in J Comput Phys 229(23):8994–9010, 2010. doi: 10.1016/j.jcp.2010.08.026 ), with a very recent approach to solving the free-space harmonic and biharmonic equations using fast Fourier transforms (FFTs) on a uniform grid (Vico et al. in J Comput Phys 323:191–203, 2016. doi: 10.1016/j.jcp.2016.07.028 ). Convolution with a truncated Gaussian function is used to place point sources on a grid. With precomputation of a scalar grid quantity that does not depend on these sources, the amount of oversampling of the grids with Gaussians can be kept at a factor of two, the minimum for aperiodic convolutions by FFTs. The resulting algorithm has a computational complexity of $$O(N \log N)$$ O ( N log N ) for problems with N sources and targets. Comparison is made with a fast multipole method to show that the performance of the new method is competitive.

Place, publisher, year, edition, pages
Springer, 2017
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-203922 (URN)10.1186/s40687-016-0092-7 (DOI)000412664600001 ()2-s2.0-85024841416 (Scopus ID)
Funder
Göran Gustafsson Foundation for Research in Natural Sciences and MedicineSwedish Research Council, 2011-3178Swedish e‐Science Research Center
Note

QC 20170411

Available from: 2017-03-20 Created: 2017-03-20 Last updated: 2024-03-18Bibliographically approved
af Klinteberg, L. & Tornberg, A.-K. (2016). A fast integral equation method for solid particles in viscous flow using quadrature by expansion. Journal of Computational Physics, 326, 420-445
Open this publication in new window or tab >>A fast integral equation method for solid particles in viscous flow using quadrature by expansion
2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 326, p. 420-445Article in journal (Refereed) Published
Abstract [en]

Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework for simulating spheroids in periodic Stokes flow, which is based on the completed double layer boundary integral formulation. The framework implements a new method known as quadrature by expansion (QBX), which uses surrogate local expansions of the layer potential to evaluate it to very high accuracy both on and off the particle surfaces. This quadrature method is accelerated through a newly developed precomputation scheme. The long range interactions are computed using the spectral Ewald (SE) fast summation method, which after integration with QBX allows the resulting system to be solved in M log M time, where M is the number of particles. This framework is suitable for simulations of large particle systems, and can be used for studying e.g. porous media models.

Place, publisher, year, edition, pages
Academic Press, 2016
Keywords
Viscous flow, Stokes equations, Boundary integral methods, Quadrature by expansion, Fast Ewald summation
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-196589 (URN)10.1016/j.jcp.2016.09.006 (DOI)000386067400023 ()2-s2.0-84988423251 (Scopus ID)
Funder
Swedish Research Council, 2011-3178Göran Gustafsson Foundation for Research in Natural Sciences and MedicineSwedish e‐Science Research Center
Note

QC 20161118

Available from: 2016-11-18 Created: 2016-11-17 Last updated: 2024-03-18Bibliographically approved
af Klinteberg, L. (2016). Ewald summation for the rotlet singularity of Stokes flow.
Open this publication in new window or tab >>Ewald summation for the rotlet singularity of Stokes flow
2016 (English)Report (Other academic)
Abstract [en]

Ewald summation is an efficient method for computing the periodic sums that appear when considering the Green's functions of Stokes flow together with periodic boundary conditions. We show how Ewald summation, and accompanying truncation error estimates, can be easily derived for the rotlet, by considering it as a superposition of electrostatic force calculations.

Publisher
p. 9
National Category
Fluid Mechanics Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-184125 (URN)
Note

QC20160407

Available from: 2016-03-28 Created: 2016-03-28 Last updated: 2025-02-05Bibliographically approved
af Klinteberg, L. (2016). Fast and accurate integral equation methods with applications in microfluidics. (Doctoral dissertation). Stockholm: KTH Royal Institute of Technology
Open this publication in new window or tab >>Fast and accurate integral equation methods with applications in microfluidics
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is concerned with computational methods for fluid flows on the microscale, also known as microfluidics. This is motivated by current research in biological physics and miniaturization technology, where there is a need to understand complex flows involving microscale structures. Numerical simulations are an important tool for doing this.

The first, and smaller, part of the thesis presents a numerical method for simulating multiphase flows involving insoluble surfactants and moving contact lines. The method is based on an interface decomposition resulting in local, Eulerian grid representations. This provides a natural setting for solving the PDE governing the surfactant concentration on the interface.

The second, and larger, part of the thesis is concerned with a framework for simulating large systems of rigid particles in three-dimensional, periodic viscous flow using a boundary integral formulation. This framework can solve the underlying flow equations to high accuracy, due to the accurate nature of surface quadrature. It is also fast, due to the natural coupling between boundary integral methods and fast summation methods.

The development of the boundary integral framework spans several different fields of numerical analysis. For fast computations of large systems, a fast Ewald summation method known as Spectral Ewald is adapted to work with the Stokes double layer potential. For accurate numerical integration, a method known as Quadrature by Expansion is developed for this same potential, and also accelerated through a scheme based on geometrical symmetries. To better understand the errors accompanying this quadrature method, an error analysis based on contour integration and calculus of residues is carried out, resulting in highly accurate error estimates.

Abstract [sv]

Denna avhandling behandlar beräkningsmetoder för strömning på mikroskalan, även känt som mikrofluidik. Detta val av ämne motiveras av aktuell forskning inom biologisk fysik och miniatyrisering, där det ofta finns ett behov av att förstå komplexa flöden med strukturer på mikroskalan. Datorsimuleringar är ett viktigt verktyg för att öka den förståelsen.

Avhandlingens första, och mindre, del beskriver en numerisk metod för att simulera flerfasflöden med olösliga surfaktanter och rörliga kontaktlinjer. Metoden är baserad på en uppdelning av gränsskiktet, som tillåter det att representeras med lokala, Euleriska nät. Detta skapar naturliga förutsättningar för lösning av den PDE som styr surfaktantkoncentrationen på gränsskiktets yta.

Avhandlingens andra, och större, del beskriver ett ramverk för att med hjälp av en randintegralformulering simulera stora system av styva partiklar i tredimensionellt, periodiskt Stokesflöde. Detta ramverk kan lösa flödesekvationerna mycket noggrant, tack vare den inneboende höga noggrannheten hos metoder för numerisk integration på släta ytor. Metoden är också snabb, tack vare den naturliga kopplingen mellan randintegralmetoder och snabba summeringsmetoder.

Utvecklingen av ramverket för partikelsimuleringar täcker ett brett spektrum av ämnet numerisk analys. För snabba beräkningar på stora system används en snabb Ewaldsummeringsmetod vid namn spektral Ewald. Denna metod har anpassats för att fungera med den randintegralformulering för Stokesflöde som används. För noggrann numerisk integration används en metod kallad expansionskvadratur (eng. Quadrature by Expansion), som också har utvecklats för att passa samma Stokesformulering. Denna metod har även gjorts snabbare genom en nyutvecklad metod baserad på geometriska symmetrier. För att bättre förstå kvadraturmetodens inneboende fel har en analys baserad på konturintegraler och residykalkyl utförts, vilket har resulterat i väldigt noggranna felestimat.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. p. 51
Series
TRITA-MAT-A ; 2016:03
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-185758 (URN)978-91-7595-962-7 (ISBN)
Public defence
2016-06-02, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2011-3178Swedish Research Council, 2007-6375
Note

QC 20160427

Available from: 2016-04-27 Created: 2016-04-26 Last updated: 2022-06-22Bibliographically approved
af Klinteberg, L., Lindbo, D. & Tornberg, A.-K. (2014). An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant. Computers & Fluids, 101, 50-63
Open this publication in new window or tab >>An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant
2014 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 101, p. 50-63Article in journal (Refereed) Published
Abstract [en]

The flow behavior of many multiphase flow applications is greatly influenced by wetting properties and the presence of surfactants. We present a numerical method for two-phase flow with insoluble surfactants and contact line dynamics in two dimensions. The method is based on decomposing the interface between two fluids into segments, which are explicitly represented on a local Eulerian grid. It provides a natural framework for treating the surfactant concentration equation, which is solved locally on each segment. An accurate numerical method for the coupled interface/surfactant system is given. The system is coupled to the Navier-Stokes equations through the immersed boundary method, and we discuss the issue of force regularization in wetting problems, when the interface touches the boundary of the domain. We use the method to illustrate how the presence of surfactants influences the behavior of free and wetting drops.

Keywords
Multiphase flow, Insoluble surfactant, Marangoni force, Moving contact line, Immersed boundary method
National Category
Fluid Mechanics
Identifiers
urn:nbn:se:kth:diva-48763 (URN)10.1016/j.compfluid.2014.05.029 (DOI)000340851500005 ()2-s2.0-84903152815 (Scopus ID)
Funder
Swedish Research Council, 621-2007-6375
Note

QC 20140919. Updated from accepted to published.

Available from: 2011-11-23 Created: 2011-11-23 Last updated: 2025-02-09Bibliographically approved
af Klinteberg, L. & Tornberg, A.-K. (2014). Fast Ewald summation for Stokesian particle suspensions. International Journal for Numerical Methods in Fluids, 76(10), 669-698
Open this publication in new window or tab >>Fast Ewald summation for Stokesian particle suspensions
2014 (English)In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 76, no 10, p. 669-698Article in journal (Refereed) Published
Abstract [en]

We present a numerical method for suspensions of spheroids of arbitrary aspect ratio, which sediment under gravity. The method is based on a periodized boundary integral formulation using the Stokes double layer potential. The resulting discrete system is solved iteratively using generalized minimal residual accelerated by the spectral Ewald method, which reduces the computational complexity to O(N log N), where N is the number of points used to discretize the particle surfaces. We develop predictive error estimates, which can be used to optimize the choice of parameters in the Ewald summation. Numerical tests show that the method is well conditioned and provides good accuracy when validated against reference solutions. 

Place, publisher, year, edition, pages
John Wiley & Sons, 2014
Keywords
viscous flows, integral equations, error estimation, microfluidics, multibody dynamics, spectral, double layer, boundary integral, ewald summation
National Category
Fluid Mechanics Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-116383 (URN)10.1002/fld.3953 (DOI)000344349000004 ()2-s2.0-84939258934 (Scopus ID)
Funder
Swedish Research Council, 2011-3178
Note

QC 20141119

Available from: 2013-01-17 Created: 2013-01-17 Last updated: 2025-02-05Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0001-7425-8029

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