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1. Dirichlet boundary value correction using Lagrange multipliers Burman, Eriket al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt1292",{id:"formSmash:items:resultList:0:j_idt1292",widgetVar:"widget_formSmash_items_resultList_0_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hansbo, PeterLarson, Mats G.Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Dirichlet boundary value correction using Lagrange multipliers2020In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 60, no 1, p. 235-260Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:0:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_0_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We propose a boundary value correction approach for cases when curved boundaries are approximated by straight lines (planes) and Lagrange multipliers are used to enforce Dirichlet boundary conditions. The approach allows for optimal order convergence for polynomial order up to 3. We show the relation to a Taylor series expansion approach previously used in the context of Nitsche's method and, in the case of inf-sup stable multiplier methods, prove a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_0_j_idt1552_0_j_idt1555",{id:"formSmash:items:resultList:0:j_idt1552:0:j_idt1555",widgetVar:"widget_formSmash_items_resultList_0_j_idt1552_0_j_idt1555",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:0:j_idt1552:0:fullText"});}); 2. One-stage exponential integrators for nonlinear Schrödinger equations over long times Cohen, David PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt1289",{id:"formSmash:items:resultList:1:j_idt1289",widgetVar:"widget_formSmash_items_resultList_1_j_idt1289",onLabel:"Cohen, David ",offLabel:"Cohen, David ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt1292",{id:"formSmash:items:resultList:1:j_idt1292",widgetVar:"widget_formSmash_items_resultList_1_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mathematisches Institut, Universität Basel.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Gauckler, LudwigInstitut für Mathematik, TU Berlin.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); One-stage exponential integrators for nonlinear Schrödinger equations over long times2012In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 52, no 4, p. 877-903Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:1:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_1_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Near-conservation over long times of the actions, of the energy, of the mass and of the momentum along the numerical solution of the cubic Schrödinger equation with small initial data is shown. Spectral discretization in space and one-stage exponential integrators in time are used. The proofs use modulated Fourier expansions.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:1:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 3. Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions Cohen, David PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt1289",{id:"formSmash:items:resultList:2:j_idt1289",widgetVar:"widget_formSmash_items_resultList_2_j_idt1289",onLabel:"Cohen, David ",offLabel:"Cohen, David ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt1292",{id:"formSmash:items:resultList:2:j_idt1292",widgetVar:"widget_formSmash_items_resultList_2_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Gauckler, LudwigTU Berlin, Germany.Hairer, ErnstUniversity of Geneva, Switzerland.Lubich, ChristianUniversity of Tübingen, Germany.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions2015In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 55, no 3, p. 705-732Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:2:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_2_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time scales that cover arbitrary negative powers of the step size. This requires non-resonance conditions between the step size and the frequencies, but in contrast to previous results the results do not require any non-resonance conditions among the frequencies. The proof uses modulated Fourier expansions with appropriately modified frequencies.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:2:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 4. Linear energy-preserving integrators for Poisson systems Cohen, David PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1289",{id:"formSmash:items:resultList:3:j_idt1289",widgetVar:"widget_formSmash_items_resultList_3_j_idt1289",onLabel:"Cohen, David ",offLabel:"Cohen, David ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1292",{id:"formSmash:items:resultList:3:j_idt1292",widgetVar:"widget_formSmash_items_resultList_3_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mathematisches Institut, Universität Basel.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hairer, ErnstSection de Mathématiques, Université de Genève.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Linear energy-preserving integrators for Poisson systems2011In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 51, no 1, p. 91-101Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:3:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_3_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge-Kutta method with infinitely many stages.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:3:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 5. Numerical energy conservation for multi-frequency oscillatory differential equations Cohen, David PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt1289",{id:"formSmash:items:resultList:4:j_idt1289",widgetVar:"widget_formSmash_items_resultList_4_j_idt1289",onLabel:"Cohen, David ",offLabel:"Cohen, David ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt1292",{id:"formSmash:items:resultList:4:j_idt1292",widgetVar:"widget_formSmash_items_resultList_4_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Section de Mathématiques, Université de Genève.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hairer, ErnstSection de Mathématiques, Université de Genève.Lubich, ChristianMathematisches Institut, Universität Tübingen.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 energy conservation for multi-frequency oscillatory differential equations2005In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 45, no 2, p. 287-305Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:4:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_4_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The long-time near-conservation of the total and oscillatory energies of numerical integrators for Hamiltonian systems with highly oscillatory solutions is studied in this paper. The numerical methods considered are symmetric trigonometric integrators and the Stormer-Verlet method. Previously obtained results for systems with a single high frequency are extended to the multi-frequency case, and new insight into the long-time behaviour of numerical solutions is gained for resonant frequencies. The results are obtained using modulated multi-frequency Fourier expansions and the Hamiltonian-like structure of the modulation system. A brief discussion of conservation properties in the continuous problem is also included.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:4:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 6. Explicit stabilised gradient descent for faster strongly convex optimisation Eftekhari, Armin PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1289",{id:"formSmash:items:resultList:5:j_idt1289",widgetVar:"widget_formSmash_items_resultList_5_j_idt1289",onLabel:"Eftekhari, Armin ",offLabel:"Eftekhari, Armin ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1292",{id:"formSmash:items:resultList:5:j_idt1292",widgetVar:"widget_formSmash_items_resultList_5_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Vandereycken, BartVilmart, GillesZygalakis, Konstantinos C.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Explicit stabilised gradient descent for faster strongly convex optimisation2021In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 61, p. 119-139Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:5:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_5_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper introduces the Runge-Kutta Chebyshev descent method (RKCD) for strongly convex optimisation problems. This new algorithm is based on explicit stabilised integrators for stiff differential equations, a powerful class of numerical schemes that avoid the severe step size restriction faced by standard explicit integrators. For optimising quadratic and strongly convex functions, this paper proves that RKCD nearly achieves the optimal convergence rate of the conjugate gradient algorithm, and the suboptimality of RKCD diminishes as the condition number of the quadratic function worsens. It is established that this optimal rate is obtained also for a partitioned variant of RKCD applied to perturbations of quadratic functions. In addition, numerical experiments on general strongly convex problems show that RKCD outperforms Nesterov's accelerated gradient descent.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:5:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_5_j_idt1552_0_j_idt1555",{id:"formSmash:items:resultList:5:j_idt1552:0:j_idt1555",widgetVar:"widget_formSmash_items_resultList_5_j_idt1552_0_j_idt1555",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:5:j_idt1552:0:fullText"});}); 7. A Faster and Simpler Recursive Algorithm for the LAPACK Routine DGELS Elmroth, Erik PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt1289",{id:"formSmash:items:resultList:6:j_idt1289",widgetVar:"widget_formSmash_items_resultList_6_j_idt1289",onLabel:"Elmroth, Erik ",offLabel:"Elmroth, Erik ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt1292",{id:"formSmash:items:resultList:6:j_idt1292",widgetVar:"widget_formSmash_items_resultList_6_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Umeå University, Faculty of Science and Technology, Department of Computing Science.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Gustavson, FredPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Faster and Simpler Recursive Algorithm for the LAPACK Routine DGELS2001In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 41, no 5, p. 936-949Article in journal (Refereed)8. Computing Periodic Deflating Subspaces Associated with a Specified Set of Eigenvalues Granat, Robert PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt1289",{id:"formSmash:items:resultList:7:j_idt1289",widgetVar:"widget_formSmash_items_resultList_7_j_idt1289",onLabel:"Granat, Robert ",offLabel:"Granat, Robert ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt1292",{id:"formSmash:items:resultList:7:j_idt1292",widgetVar:"widget_formSmash_items_resultList_7_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, HPC2N (High Performance Computing Centre North).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kågström, BoUmeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, HPC2N (High Performance Computing Centre North).Kressner, DanielETH Zürich.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Computing Periodic Deflating Subspaces Associated with a Specified Set of Eigenvalues2007In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 47, no 4, p. 763-791Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:7:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_7_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular K-cyclic matrix pair sequence (A (k) ,E (k) ). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvester-like equation and constructing K pairs of orthogonal matrices. These pairs define an orthogonal K-cyclic equivalence transformation that swaps adjacent diagonal blocks in the Schur form. An error analysis of this swapping procedure is presented, which extends existing results for reordering eigenvalues in the generalized real Schur form of a regular pair (A,E). Our direct reordering method is used to compute periodic deflating subspace pairs corresponding to a specified set of eigenvalues. This computational task arises in various applications related to discrete-time periodic descriptor systems. Computational experiments confirm the stability and reliability of the presented eigenvalue reordering method.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 9. A numerical evaluation of solvers for the periodic riccati differential equation Gusev, Sergei PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt1289",{id:"formSmash:items:resultList:8:j_idt1289",widgetVar:"widget_formSmash_items_resultList_8_j_idt1289",onLabel:"Gusev, Sergei ",offLabel:"Gusev, Sergei ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt1292",{id:"formSmash:items:resultList:8:j_idt1292",widgetVar:"widget_formSmash_items_resultList_8_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Johansson, StefanUmeå University, Faculty of Science and Technology, Department of Computing Science.Kågström, BoUmeå University, Faculty of Science and Technology, Department of Computing Science.Shiriaev, AntonUmeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.Varga, AndrasInstitute of Robotics and Mechatronics, German Aerospace Center, DLR, Germany.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A numerical evaluation of solvers for the periodic riccati differential equation2010In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 50, no 2, p. 301-329Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:8:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_8_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Efficient and accurate structure exploiting numerical methods for solvingthe periodic Riccati differential equation (PRDE) are addressed. Such methods areessential, for example, to design periodic feedback controllers for periodic controlsystems. Three recently proposed methods for solving the PRDE are presented andevaluated on challenging periodic linear artificial systems with known solutions and applied to the stabilization of periodic motions of mechanical systems. The first twomethods are of the type multiple shooting and rely on computing the stable invariantsubspace of an associated Hamiltonian system. The stable subspace is determinedusing either algorithms for computing an ordered periodic real Schur form of a cyclicmatrix sequence, or a recently proposed method which implicitly constructs a stabledeflating subspace from an associated lifted pencil. The third method reformulatesthe PRDE as a convex optimization problem where the stabilizing solution is approximatedby its truncated Fourier series. As known, this reformulation leads to a semidefiniteprogramming problem with linear matrix inequality constraints admitting aneffective numerical realization. The numerical evaluation of the PRDE methods, withfocus on the number of states (n) and the length of the period (T ) of the periodicsystems considered, includes both quantitative and qualitative results.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions Holst, Michael J. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt1289",{id:"formSmash:items:resultList:9:j_idt1289",widgetVar:"widget_formSmash_items_resultList_9_j_idt1289",onLabel:"Holst, Michael J. ",offLabel:"Holst, Michael J. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt1292",{id:"formSmash:items:resultList:9:j_idt1292",widgetVar:"widget_formSmash_items_resultList_9_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of California at San Diego, La Jolla, CA 92093-0112, USA.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Larson, Mats G.Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.Målqvist, AxelDepartment of Information Technology, Uppsala University, 751 05 Uppsala, Sweden.Söderlund, RobertUmeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions2010In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 50, no 4, p. 781-795Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:9:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_9_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper we present a finite element discretization of the Joule-heating problem. We prove existence of solution to the discrete formulation and strong convergence of the finite element solution to the weak solution, up to a sub-sequence. We also present numerical examples in three spatial dimensions. The first example demonstrates the convergence of the method in the second example we consider an engineering application.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Retracing the residual curve of a Lyapunov equation solver Kjelgaard Mikkelsen, Carl Christian PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt1289",{id:"formSmash:items:resultList:10:j_idt1289",widgetVar:"widget_formSmash_items_resultList_10_j_idt1289",onLabel:"Kjelgaard Mikkelsen, Carl Christian ",offLabel:"Kjelgaard Mikkelsen, Carl Christian ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Retracing the residual curve of a Lyapunov equation solver2011In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 51, no 4, p. 959-975Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:10:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_10_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Let A ∈ Rn×n and let B ∈ Rn×p and consider the Lyapunov matrix equation AX + XAT + BBT = 0. If A + AT < 0, then the extended Krylov subspacemethod (EKSM) can be used to compute a sequence of low rank approximations of X. In this paper we show how to construct a symmetric negative definite matrix A and a column vector B, for which the EKSM generates a predetermined residual curve.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:10:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_10_j_idt1552_0_j_idt1555",{id:"formSmash:items:resultList:10:j_idt1552:0:j_idt1555",widgetVar:"widget_formSmash_items_resultList_10_j_idt1552_0_j_idt1555",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:10:j_idt1552:0:fullText"});}); 12. A uniformly well-conditioned, unfitted Nitsche method for interface problems Wadbro, Eddie PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt1289",{id:"formSmash:items:resultList:11:j_idt1289",widgetVar:"widget_formSmash_items_resultList_11_j_idt1289",onLabel:"Wadbro, Eddie ",offLabel:"Wadbro, Eddie ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt1292",{id:"formSmash:items:resultList:11:j_idt1292",widgetVar:"widget_formSmash_items_resultList_11_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Umeå University, Faculty of Science and Technology, Department of Computing Science.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Zahedi, SaraDepartment of Information Technology, Uppsala University, Uppsala.Kreiss, GunillaDepartment of Information Technology, Uppsala University, Uppsala.Berggren, MartinUmeå University, Faculty of Science and Technology, Department of Computing Science.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A uniformly well-conditioned, unfitted Nitsche method for interface problems2013In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 53, no 3, p. 791-820Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:11:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_11_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A finite element method for elliptic partial differential equations that allows for discontinuities along an interface not aligned with the mesh is presented. The solution on each side of the interface is separately expanded in standard continuous, piecewise-linear functions, and jump conditions at the interface are weakly enforced using a variant of Nitsche’s method. In our method, the solutions on each side of the interface are extended to the entire domain which results in a fixed number of unknowns independent of the location of the interface. A stabilization procedure is included to ensure well-defined extensions. We prove that the method provides optimal convergence order in the energy and the

*L*^{2}norms and a condition number of the system matrix that is independent of the position of the interface relative to the mesh. Numerical experiments confirm the theoretical results and demonstrate optimal convergence order also for the pointwise errors.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:11:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500});

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