Edit Profile (opens in new tab) Praetorius, Dirk Compute Distance To: Compute Author ID: praetorius.dirk Published as: Praetorius, Dirk; Praetorius, D. External Links: MGP · ORCID Documents Indexed: 120 Publications since 2002, including 1 Book 1 Contribution as Editor Co-Authors: 71 Co-Authors with 119 Joint Publications 1,401 Co-Co-Authors all top 5 Co-Authors 2 single-authored 27 Feischl, Michael 22 Führer, Thomas 17 Gantner, Gregor 16 Karkulik, Michael 16 Melenk, Jens Markus 13 Ruggeri, Michele 12 Aurada, Markus 11 Carstensen, Carsten 10 Haberl, Alexander 10 Page, Marcus 9 Erath, Christoph 7 Ferraz-Leite, Samuel 6 Bespalov, Alexei 6 Innerberger, Michael 6 Schimanko, Stefan 5 Di Fratta, Giovanni 5 Faustmann, Markus 5 Pfeiler, Carl-Martin 5 Popović, Nikola 5 Stephan, Ernst Peter 5 Stiftner, Bernhard 4 Becker, Roland 4 Funken, Stefan A. 4 Goldenits, Petra 3 Betcke, Timo 3 Schlömerkemper, Anja 2 Baňas, Ľubomír 2 Hrkac, Gino 2 Koch, Othmar 2 Mayr, Markus 2 Ortner, Christoph 2 Pavlicek, David 2 Repin, Sergeĭ Igorevich 2 Rocchi, Leonardo 2 Suess, Dieter 2 Weinmüller, Ewa B. 1 Abert, Claas 1 Amad, Alan A. S. 1 Auzinger, Winfried 1 Bruckner, F. 1 Brunner, Maximilian 1 Davoli, Elisa 1 Ebner, Michael 1 Haberlik, Daniel 1 Heid, Pascal 1 Heuer, Norbert 1 Jüngel, Ansgar 1 Katzenbeisser, Stefan 1 Kemetmüller, J. 1 Kraus, Johannes K. 1 Kurz, Stefan 1 Le, Kim-Ngan 1 Ledger, Paul David 1 Maischak, Matthias 1 März, Roswitha 1 Mauser, Norbert Julius 1 Mitscha-Eibl, Gregor 1 Of, Günther 1 Pauly, Dirk 1 Rieder, Alexander 1 Rochat, Jonathan 1 Sauter, Stefan A. 1 Sebastian, Daniel 1 Segatti, Antonio 1 Slastikov, Valeriy V. 1 Überhuber, Christoph W. 1 van der Zee, Kristoffer George 1 Vohralík, Martin 1 Wihler, Thomas Pascal 1 Wissgott, Philipp 1 Wohlmuth, Barbara I. all top 5 Serials 11 Numerische Mathematik 9 Computers & Mathematics with Applications 9 SIAM Journal on Numerical Analysis 8 Computational Methods in Applied Mathematics 7 Computer Methods in Applied Mechanics and Engineering 7 IMA Journal of Numerical Analysis 6 Mathematics of Computation 6 Applied Numerical Mathematics 5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Applicable Analysis 3 SIAM Journal on Scientific Computing 3 Engineering Analysis with Boundary Elements 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Journal of Computational Physics 2 Calcolo 2 Computing 2 Journal of Computational and Applied Mathematics 2 Constructive Approximation 2 Computational Mechanics 2 Numerical Methods for Partial Differential Equations 2 Numerical Algorithms 2 Continuum Mechanics and Thermodynamics 2 ETNA. Electronic Transactions on Numerical Analysis 1 Mathematical Methods in the Applied Sciences 1 Colloquium Mathematicum 1 Journal of Differential Equations 1 Zeitschrift für Analysis und ihre Anwendungen 1 Computer Aided Geometric Design 1 Journal of Integral Equations and Applications 1 Applied Mathematical Modelling 1 Advances in Computational Mathematics 1 Nonlinear Analysis. Real World Applications 1 Archives of Computational Methods in Engineering 1 Journal of Numerical Mathematics 1 International Journal of Numerical Analysis and Modeling 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Fields 112 Numerical analysis (65-XX) 51 Partial differential equations (35-XX) 19 Optics, electromagnetic theory (78-XX) 10 Approximations and expansions (41-XX) 10 Integral equations (45-XX) 8 Statistical mechanics, structure of matter (82-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Mechanics of deformable solids (74-XX) 4 Computer science (68-XX) 2 Real functions (26-XX) 2 Ordinary differential equations (34-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 107 Publications have been cited 1,160 times in 417 Documents Cited by ▼ Year ▼ Axioms of adaptivity. Zbl 1350.65119Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D. 112 2014 Efficient implementation of adaptive P1-FEM in Matlab. Zbl 1284.65197Funken, Stefan; Praetorius, Dirk; Wissgott, Philipp 46 2011 On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection. Zbl 1302.65267Karkulik, Michael; Pavlicek, David; Praetorius, Dirk 46 2013 Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems. Zbl 1300.65086Feischl, M.; Führer, T.; Praetorius, D. 39 2014 Quasi-optimal convergence rate for an adaptive boundary element method. Zbl 1273.65186Feischl, M.; Karkulik, M.; Melenk, J. M.; Praetorius, D. 37 2013 Residual-based a posteriori error estimate for hypersingular equation on surfaces. Zbl 1063.65116Carstensen, Carsten; Maischak, M.; Praetorius, D.; Stephan, E. P. 31 2004 Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity. Zbl 1312.74031Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk 26 2013 Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods. Zbl 1285.65070Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk 25 2013 Simple a posteriori error estimators for the \(h\)-version of the boundary element method. Zbl 1175.65126Ferraz-Leite, S.; Praetorius, D. 25 2008 Convergence of simple adaptive Galerkin schemes based on \(h - h/2\) error estimators. Zbl 1198.65213Ferraz-Leite, S.; Ortner, C.; Praetorius, D. 24 2010 An abstract analysis of optimal goal-oriented adaptivity. Zbl 1382.65392Feischl, Michael; Praetorius, Dirk; van der Zee, Kristoffer G. 24 2016 Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. Zbl 1105.65124Carstensen, Carsten; Praetorius, Dirk 24 2006 Energy norm based a posteriori error estimation for boundary element methods in two dimensions. Zbl 1177.65192Erath, C.; Ferraz-Leite, S.; Funken, S.; Praetorius, D. 21 2009 Estimator reduction and convergence of adaptive BEM. Zbl 1237.65131Aurada, Markus; Ferraz-Leite, Samuel; Praetorius, Dirk 20 2012 Adaptive IGAFEM with optimal convergence rates: hierarchical B-splines. Zbl 1376.41006Gantner, Gregor; Haberlik, Daniel; Praetorius, Dirk 20 2017 Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation. Zbl 1314.65161Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk 18 2014 Energy norm based error estimators for adaptive BEM for hypersingular integral equations. Zbl 1320.65184Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk 18 2015 Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D. Zbl 1278.65168Erath, C.; Funken, S.; Goldenits, P.; Praetorius, D. 17 2013 Local inverse estimates for non-local boundary integral operators. Zbl 1368.65242Aurada, M.; Feischl, M.; Führer, T.; Karkulik, M.; Melenk, J. M.; Praetorius, D. 17 2017 Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. Zbl 1362.65131Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk 17 2017 Averaging techniques for the a posteriori BEM error control for a hypersingular integral equation in two dimensions. Zbl 1140.65089Carstensen, Carsten; Praetorius, Dirk 17 2007 Adaptive 2D IGA boundary element methods. Zbl 1403.65267Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk 16 2016 Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations. Zbl 1425.65200Feischl, Michael; Gantner, Gregor; Praetorius, Dirk 16 2015 Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation. Zbl 1312.65173Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, J. Markus; Praetorius, Dirk 16 2015 HILBERT – a MATLAB implementation of adaptive 2D-BEM. \(\underline {\text H}\)ilbert \(\underline {\text I}\)s a \(\underline {\text L}\)ovely \(\underline {\text B}\)oundary \(\underline {\text E}\)lement \(\underline {\text R}\)esearch \(\underline {\text T}\)ool. Zbl 1298.65183Aurada, Markus; Ebner, Michael; Feischl, Michael; Ferraz-Leite, Samuel; Führer, Thomas; Goldenits, Petra; Karkulik, Michael; Mayr, Markus; Praetorius, Dirk 15 2014 Each \(H^{1/2}\)-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in \(\mathbb R^d\). Zbl 1275.65078Aurada, M.; Feischl, M.; Kemetmüller, J.; Page, M.; Praetorius, D. 14 2013 Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation. Zbl 1348.65172Feischl, Michael; Führer, Thomas; Heuer, Norbert; Karkulik, Michael; Praetorius, Dirk 14 2015 Rate optimal adaptive FEM with inexact solver for nonlinear operators. Zbl 1477.65212Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Stiftner, Bernhard 14 2018 Spin-polarized transport in ferromagnetic multilayers: an unconditionally convergent FEM integrator. Zbl 1361.82041Abert, Claas; Hrkac, Gino; Page, Marcus; Praetorius, Dirk; Ruggeri, Michele; Suess, Dieter 14 2014 Multiscale modeling in micromagnetics: existence of solutions and numerical integration. Zbl 1320.35336Bruckner, F.; Suess, D.; Feischl, M.; Führer, T.; Goldenits, P.; Page, M.; Praetorius, D.; Ruggeri, M. 13 2014 Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. Zbl 1291.65341Feischl, M.; Page, M.; Praetorius, D. 13 2014 \(\mathcal {H}\)-matrix approximability of the inverses of FEM matrices. Zbl 1334.65192Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk 13 2015 Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems. Zbl 1276.65066Aurada, Markus; Feischl, Michael; Praetorius, Dirk 12 2012 Averaging techniques for a posteriori error control in finite element and boundary element analysis. Zbl 1298.65161Carstensen, Carsten; Praetorius, Dirk 11 2007 Dörfler marking with minimal cardinality is a linear complexity problem. Zbl 1446.65190Pfeiler, Carl-Martin; Praetorius, Dirk 11 2020 Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems. Zbl 1439.65148Bespalov, Alex; Haberl, Alexander; Praetorius, Dirk 11 2017 Analysis of the operator \(\Delta^{-1}\text{div}\) arising in magnetic models. Zbl 1137.35342Praetorius, Dirk 11 2004 Numerical analysis for a macroscopic model in micromagnetics. Zbl 1088.78009Carstensen, Carsten; Praetorius, Dirk 10 2005 Adaptive BEM with inexact PCG solver yields almost optimal computational costs. Zbl 1412.65233Führer, Thomas; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan 10 2019 On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems. Zbl 1232.49034Ortner, Christoph; Praetorius, Dirk 9 2011 Existence of \(\mathcal{H}\)-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Zbl 1327.65253Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk 9 2016 A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations. Zbl 1327.65233Baňas, Lubomir; Page, Marcus; Praetorius, Dirk 9 2015 On a decoupled linear FEM integrator for eddy-current-LLG. Zbl 1316.65087Le, Kim-Ngan; Page, Marcus; Praetorius, Dirk; Tran, Thanh 9 2015 Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Zbl 1409.65075Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard 9 2018 Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without \(h\)-weighting factor. Zbl 1303.65091Feischl, Michael; Führer, Thomas; Mitscha-Eibl, Gregor; Praetorius, Dirk; Stephan, Ernst P. 8 2014 Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement. Zbl 1280.65116Karkulik, Michael; Of, Günther; Praetorius, Dirk 8 2013 Convergence of adaptive stochastic Galerkin FEM. Zbl 1425.65146Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele 8 2019 Adaptive boundary element methods for optimal convergence of point errors. Zbl 1338.65259Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Führer, Thomas 8 2016 Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation. Zbl 1466.65127Di Fratta, Giovanni; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard 7 2020 Existence of \(\mathcal{H}\)-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. Zbl 1433.65324Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk 7 2017 A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction. Zbl 1334.78040Baňas, Ľubomír; Page, Marcus; Praetorius, Dirk; Rochat, Jonathan 7 2014 Collocation methods for index 1 DAEs with a singularity of the first kind. Zbl 1196.65134Koch, Othmar; März, Roswitha; Praetorius, Dirk; Weinmüller, Ewa 7 2010 Convergence of adaptive boundary element methods. Zbl 1238.65124Carstensen, Carsten; Praetorius, Dirk 7 2012 Adaptive vertex-centered finite volume methods with convergence rates. Zbl 1416.65410Erath, Christoph; Praetorius, Dirk 7 2016 Applications of \(\mathcal H\)-matrix techniques in micromagnetics. Zbl 1070.78011Popović, N.; Praetorius, D. 7 2005 Adaptive isogeometric boundary element methods with local smoothness control. Zbl 07205673Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan 7 2020 Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations. Zbl 1372.65317Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P. 6 2017 A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling. Zbl 1245.65154Aurada, M.; Feischl, M.; Karkulik, M.; Praetorius, Dirk 6 2012 Convergence of adaptive BEM for some mixed boundary value problem. Zbl 1242.65220Aurada, M.; Ferraz-Leite, S.; Goldenits, P.; Karkulik, M.; Mayr, M.; Praetorius, D. 6 2012 ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve. Zbl 1287.65102Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk 6 2014 Effective simulation of a macroscopic model for stationary micromagnetics. Zbl 1063.78016Carstensen, Carsten; Praetorius, Dirk 6 2005 Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs. Zbl 1440.65184Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele 6 2019 Simultaneous quasi-optimal convergence rates in FEM-BEM coupling. Zbl 1359.65263Melenk, J. M.; Praetorius, D.; Wohlmuth, B. 6 2017 Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. Zbl 1415.78008Hrkac, Gino; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Segatti, Antonio; Stiftner, Bernhard 6 2019 New a posteriori error estimates for singular boundary value problems. Zbl 1082.65079Auzinger, Winfried; Koch, Othmar; Praetorius, Dirk; Weinmüller, Ewa 5 2005 A posteriori error estimate and adaptive mesh refinement for the cell-centered finite volume method for elliptic boundary value problems. Zbl 1188.65148Erath, Christoph; Praetorius, Dirk 5 2009 Convergence of adaptive FEM for some elliptic obstacle problem. Zbl 1262.65156Page, M.; Praetorius, D. 5 2013 Adaptive IGAFEM with optimal convergence rates: T-splines. Zbl 07242739Gantner, Gregor; Praetorius, Dirk 5 2020 Energy contraction and optimal convergence of adaptive iterative linearized finite element methods. Zbl 1480.35214Heid, Pascal; Praetorius, Dirk; Wihler, Thomas P. 5 2021 Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems. Zbl 1439.74410Feischl, M.; Führer, T.; Karkulik, M.; Praetorius, D. 5 2015 Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements. Zbl 1365.65253Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P. 5 2017 Adaptive BEM with optimal convergence rates for the Helmholtz equation. Zbl 1440.65259Bespalov, Alex; Betcke, Timo; Haberl, Alexander; Praetorius, Dirk 5 2019 Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods. Zbl 1441.65114Führer, Thomas; Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan 5 2019 Optimal convergence behavior of adaptive FEM driven by simple \((h-h/2)\)-type error estimators. Zbl 1443.65294Erath, Christoph; Gantner, Gregor; Praetorius, Dirk 4 2020 Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics. Zbl 1451.35205Di Fratta, Giovanni; Innerberger, Michael; Praetorius, Dirk 4 2020 A posteriori error control in adaptive qualocation boundary element analysis for a logarithmic-kernel integral equation of the first kind. Zbl 1042.65084Carstensen, Carsten; Praetorius, Dirk 4 2003 Optimal convergence rates for goal-oriented FEM with quadratic goal functional. Zbl 1476.65290Becker, Roland; Innerberger, Michael; Praetorius, Dirk 4 2021 Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data. Zbl 1310.65144Feischl, Michael; Page, Marcus; Praetorius, Dirk 4 2014 A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems. Zbl 1415.65247Führer, Thomas; Praetorius, Dirk 4 2018 Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra. Zbl 1453.78012Betcke, Timo; Haberl, Alexander; Praetorius, Dirk 3 2019 Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Zbl 1478.65121Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk 3 2021 Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Zbl 1263.78017Ferraz-Leite, Samuel; Melenk, Jens Markus; Praetorius, Dirk 3 2012 FEM-BEM coupling for the large-body limit in micromagnetics. Zbl 1310.78014Aurada, M.; Melenk, J. M.; Praetorius, D. 3 2015 Rate optimality of adaptive finite element methods with respect to overall computational costs. Zbl 1468.65189Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan 3 2021 Optimal adaptivity for the SUPG finite element method. Zbl 1441.65101Erath, Christoph; Praetorius, Dirk 3 2019 Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. I: Analysis. Zbl 1160.74355Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja 3 2007 Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. II: Numerical simulation. Zbl 1160.74356Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja 3 2007 Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations. Zbl 1466.65167Erath, Christoph; Praetorius, Dirk 2 2019 Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Zbl 1468.65191Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan; Vohralík, Martin 2 2021 Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy. Zbl 1247.78051Carstensen, C.; Praetorius, D. 2 2012 A short note on plain convergence of adaptive least-squares finite element methods. Zbl 1451.65189Führer, Thomas; Praetorius, Dirk 2 2020 Mixed conforming elements for the large-body limit in micromagnetics. Zbl 1285.65076Aurada, Markus; Melenk, Jens M.; Praetorius, Dirk 2 2014 A new proof for existence of \(\mathcal H\)-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian. Zbl 1282.65153Faustmann, Markus; Melenk, Jens M.; Praetorius, Dirk 2 2014 Adaptive Uzawa algorithm for the Stokes equation. Zbl 1434.65248Di Fratta, Giovanni; Führer, Thomas; Gantner, Gregor; Praetorius, Dirk 2 2019 Instance-optimal goal-oriented adaptivity. Zbl 1474.65440Innerberger, Michael; Praetorius, Dirk 2 2021 Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. Zbl 1453.82102Kraus, Johannes; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard 1 2019 Céa-type quasi-optimality and convergence rates for (adaptive) vertex-centered FVM. Zbl 1372.65294Erath, Christoph; Praetorius, Dirk 1 2017 Remarks and examples concerning distance ellipsoids. Zbl 1017.46006Praetorius, Dirk 1 2002 Magnetic force formulae for magnets at small distances. Zbl 1391.78003Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja 1 2005 The saturation assumption yields optimal convergence of two-level adaptive BEM. Zbl 1440.65263Praetorius, Dirk; Ruggeri, Michele; Stephan, Ernst P. 1 2020 Adaptive BEM for elliptic PDE systems. I: Abstract framework, for weakly-singular integral equations. Zbl 1490.65248Gantner, Gregor; Praetorius, Dirk 1 2022 Plain convergence of adaptive algorithms without exploiting reliability and efficiency. Zbl 07524720Gantner, Gregor; Praetorius, Dirk 1 2022 Adaptive BEM for elliptic PDE systems. II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations. Zbl 1490.65299Gantner, Gregor; Praetorius, Dirk 1 2022 Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction. Zbl 1492.78005Davoli, Elisa; Di Fratta, Giovanni; Praetorius, Dirk; Ruggeri, Michele 1 2022 Energy contraction and optimal convergence of adaptive iterative linearized finite element methods. Zbl 1480.35214Heid, Pascal; Praetorius, Dirk; Wihler, Thomas P. 5 2021 Optimal convergence rates for goal-oriented FEM with quadratic goal functional. Zbl 1476.65290Becker, Roland; Innerberger, Michael; Praetorius, Dirk 4 2021 Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Zbl 1478.65121Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk 3 2021 Rate optimality of adaptive finite element methods with respect to overall computational costs. Zbl 1468.65189Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan 3 2021 Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Zbl 1468.65191Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan; Vohralík, Martin 2 2021 Instance-optimal goal-oriented adaptivity. Zbl 1474.65440Innerberger, Michael; Praetorius, Dirk 2 2021 Dörfler marking with minimal cardinality is a linear complexity problem. Zbl 1446.65190Pfeiler, Carl-Martin; Praetorius, Dirk 11 2020 Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation. Zbl 1466.65127Di Fratta, Giovanni; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard 7 2020 Adaptive isogeometric boundary element methods with local smoothness control. Zbl 07205673Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan 7 2020 Adaptive IGAFEM with optimal convergence rates: T-splines. Zbl 07242739Gantner, Gregor; Praetorius, Dirk 5 2020 Optimal convergence behavior of adaptive FEM driven by simple \((h-h/2)\)-type error estimators. Zbl 1443.65294Erath, Christoph; Gantner, Gregor; Praetorius, Dirk 4 2020 Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics. Zbl 1451.35205Di Fratta, Giovanni; Innerberger, Michael; Praetorius, Dirk 4 2020 A short note on plain convergence of adaptive least-squares finite element methods. Zbl 1451.65189Führer, Thomas; Praetorius, Dirk 2 2020 The saturation assumption yields optimal convergence of two-level adaptive BEM. Zbl 1440.65263Praetorius, Dirk; Ruggeri, Michele; Stephan, Ernst P. 1 2020 Adaptive BEM with inexact PCG solver yields almost optimal computational costs. Zbl 1412.65233Führer, Thomas; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan 10 2019 Convergence of adaptive stochastic Galerkin FEM. Zbl 1425.65146Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele 8 2019 Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs. Zbl 1440.65184Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele 6 2019 Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. Zbl 1415.78008Hrkac, Gino; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Segatti, Antonio; Stiftner, Bernhard 6 2019 Adaptive BEM with optimal convergence rates for the Helmholtz equation. Zbl 1440.65259Bespalov, Alex; Betcke, Timo; Haberl, Alexander; Praetorius, Dirk 5 2019 Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods. Zbl 1441.65114Führer, Thomas; Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan 5 2019 Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra. Zbl 1453.78012Betcke, Timo; Haberl, Alexander; Praetorius, Dirk 3 2019 Optimal adaptivity for the SUPG finite element method. Zbl 1441.65101Erath, Christoph; Praetorius, Dirk 3 2019 Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations. Zbl 1466.65167Erath, Christoph; Praetorius, Dirk 2 2019 Adaptive Uzawa algorithm for the Stokes equation. Zbl 1434.65248Di Fratta, Giovanni; Führer, Thomas; Gantner, Gregor; Praetorius, Dirk 2 2019 Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. Zbl 1453.82102Kraus, Johannes; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard 1 2019 Rate optimal adaptive FEM with inexact solver for nonlinear operators. Zbl 1477.65212Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Stiftner, Bernhard 14 2018 Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Zbl 1409.65075Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard 9 2018 A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems. Zbl 1415.65247Führer, Thomas; Praetorius, Dirk 4 2018 Adaptive IGAFEM with optimal convergence rates: hierarchical B-splines. Zbl 1376.41006Gantner, Gregor; Haberlik, Daniel; Praetorius, Dirk 20 2017 Local inverse estimates for non-local boundary integral operators. Zbl 1368.65242Aurada, M.; Feischl, M.; Führer, T.; Karkulik, M.; Melenk, J. M.; Praetorius, D. 17 2017 Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. Zbl 1362.65131Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk 17 2017 Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems. Zbl 1439.65148Bespalov, Alex; Haberl, Alexander; Praetorius, Dirk 11 2017 Existence of \(\mathcal{H}\)-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. Zbl 1433.65324Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk 7 2017 Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations. Zbl 1372.65317Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P. 6 2017 Simultaneous quasi-optimal convergence rates in FEM-BEM coupling. Zbl 1359.65263Melenk, J. M.; Praetorius, D.; Wohlmuth, B. 6 2017 Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements. Zbl 1365.65253Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P. 5 2017 Céa-type quasi-optimality and convergence rates for (adaptive) vertex-centered FVM. Zbl 1372.65294Erath, Christoph; Praetorius, Dirk 1 2017 An abstract analysis of optimal goal-oriented adaptivity. Zbl 1382.65392Feischl, Michael; Praetorius, Dirk; van der Zee, Kristoffer G. 24 2016 Adaptive 2D IGA boundary element methods. Zbl 1403.65267Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk 16 2016 Existence of \(\mathcal{H}\)-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Zbl 1327.65253Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk 9 2016 Adaptive boundary element methods for optimal convergence of point errors. Zbl 1338.65259Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Führer, Thomas 8 2016 Adaptive vertex-centered finite volume methods with convergence rates. Zbl 1416.65410Erath, Christoph; Praetorius, Dirk 7 2016 Energy norm based error estimators for adaptive BEM for hypersingular integral equations. Zbl 1320.65184Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk 18 2015 Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations. Zbl 1425.65200Feischl, Michael; Gantner, Gregor; Praetorius, Dirk 16 2015 Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation. Zbl 1312.65173Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, J. Markus; Praetorius, Dirk 16 2015 Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation. Zbl 1348.65172Feischl, Michael; Führer, Thomas; Heuer, Norbert; Karkulik, Michael; Praetorius, Dirk 14 2015 \(\mathcal {H}\)-matrix approximability of the inverses of FEM matrices. Zbl 1334.65192Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk 13 2015 A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations. Zbl 1327.65233Baňas, Lubomir; Page, Marcus; Praetorius, Dirk 9 2015 On a decoupled linear FEM integrator for eddy-current-LLG. Zbl 1316.65087Le, Kim-Ngan; Page, Marcus; Praetorius, Dirk; Tran, Thanh 9 2015 Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems. Zbl 1439.74410Feischl, M.; Führer, T.; Karkulik, M.; Praetorius, D. 5 2015 FEM-BEM coupling for the large-body limit in micromagnetics. Zbl 1310.78014Aurada, M.; Melenk, J. M.; Praetorius, D. 3 2015 Erratum to: “On 2D newest vertex bisection: optimality of mesh-closure and \(H^1\)-stability of \(L_2\)-projection”. Zbl 1331.65167Karkulik, Michael; Pavlicek, David; Praetorius, Dirk 1 2015 Axioms of adaptivity. Zbl 1350.65119Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D. 112 2014 Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems. Zbl 1300.65086Feischl, M.; Führer, T.; Praetorius, D. 39 2014 Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation. Zbl 1314.65161Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk 18 2014 HILBERT – a MATLAB implementation of adaptive 2D-BEM. \(\underline {\text H}\)ilbert \(\underline {\text I}\)s a \(\underline {\text L}\)ovely \(\underline {\text B}\)oundary \(\underline {\text E}\)lement \(\underline {\text R}\)esearch \(\underline {\text T}\)ool. Zbl 1298.65183Aurada, Markus; Ebner, Michael; Feischl, Michael; Ferraz-Leite, Samuel; Führer, Thomas; Goldenits, Petra; Karkulik, Michael; Mayr, Markus; Praetorius, Dirk 15 2014 Spin-polarized transport in ferromagnetic multilayers: an unconditionally convergent FEM integrator. Zbl 1361.82041Abert, Claas; Hrkac, Gino; Page, Marcus; Praetorius, Dirk; Ruggeri, Michele; Suess, Dieter 14 2014 Multiscale modeling in micromagnetics: existence of solutions and numerical integration. Zbl 1320.35336Bruckner, F.; Suess, D.; Feischl, M.; Führer, T.; Goldenits, P.; Page, M.; Praetorius, D.; Ruggeri, M. 13 2014 Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. Zbl 1291.65341Feischl, M.; Page, M.; Praetorius, D. 13 2014 Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without \(h\)-weighting factor. Zbl 1303.65091Feischl, Michael; Führer, Thomas; Mitscha-Eibl, Gregor; Praetorius, Dirk; Stephan, Ernst P. 8 2014 A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction. Zbl 1334.78040Baňas, Ľubomír; Page, Marcus; Praetorius, Dirk; Rochat, Jonathan 7 2014 ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve. Zbl 1287.65102Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk 6 2014 Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data. Zbl 1310.65144Feischl, Michael; Page, Marcus; Praetorius, Dirk 4 2014 Mixed conforming elements for the large-body limit in micromagnetics. Zbl 1285.65076Aurada, Markus; Melenk, Jens M.; Praetorius, Dirk 2 2014 A new proof for existence of \(\mathcal H\)-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian. Zbl 1282.65153Faustmann, Markus; Melenk, Jens M.; Praetorius, Dirk 2 2014 On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection. Zbl 1302.65267Karkulik, Michael; Pavlicek, David; Praetorius, Dirk 46 2013 Quasi-optimal convergence rate for an adaptive boundary element method. Zbl 1273.65186Feischl, M.; Karkulik, M.; Melenk, J. M.; Praetorius, D. 37 2013 Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity. Zbl 1312.74031Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk 26 2013 Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods. Zbl 1285.65070Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk 25 2013 Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D. Zbl 1278.65168Erath, C.; Funken, S.; Goldenits, P.; Praetorius, D. 17 2013 Each \(H^{1/2}\)-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in \(\mathbb R^d\). Zbl 1275.65078Aurada, M.; Feischl, M.; Kemetmüller, J.; Page, M.; Praetorius, D. 14 2013 Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement. Zbl 1280.65116Karkulik, Michael; Of, Günther; Praetorius, Dirk 8 2013 Convergence of adaptive FEM for some elliptic obstacle problem. Zbl 1262.65156Page, M.; Praetorius, D. 5 2013 Estimator reduction and convergence of adaptive BEM. Zbl 1237.65131Aurada, Markus; Ferraz-Leite, Samuel; Praetorius, Dirk 20 2012 Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems. Zbl 1276.65066Aurada, Markus; Feischl, Michael; Praetorius, Dirk 12 2012 Convergence of adaptive boundary element methods. Zbl 1238.65124Carstensen, Carsten; Praetorius, Dirk 7 2012 A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling. Zbl 1245.65154Aurada, M.; Feischl, M.; Karkulik, M.; Praetorius, Dirk 6 2012 Convergence of adaptive BEM for some mixed boundary value problem. Zbl 1242.65220Aurada, M.; Ferraz-Leite, S.; Goldenits, P.; Karkulik, M.; Mayr, M.; Praetorius, D. 6 2012 Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Zbl 1263.78017Ferraz-Leite, Samuel; Melenk, Jens Markus; Praetorius, Dirk 3 2012 Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy. Zbl 1247.78051Carstensen, C.; Praetorius, D. 2 2012 Efficient implementation of adaptive P1-FEM in Matlab. Zbl 1284.65197Funken, Stefan; Praetorius, Dirk; Wissgott, Philipp 46 2011 On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems. Zbl 1232.49034Ortner, Christoph; Praetorius, Dirk 9 2011 Convergence of simple adaptive Galerkin schemes based on \(h - h/2\) error estimators. Zbl 1198.65213Ferraz-Leite, S.; Ortner, C.; Praetorius, D. 24 2010 Collocation methods for index 1 DAEs with a singularity of the first kind. Zbl 1196.65134Koch, Othmar; März, Roswitha; Praetorius, Dirk; Weinmüller, Ewa 7 2010 Energy norm based a posteriori error estimation for boundary element methods in two dimensions. Zbl 1177.65192Erath, C.; Ferraz-Leite, S.; Funken, S.; Praetorius, D. 21 2009 A posteriori error estimate and adaptive mesh refinement for the cell-centered finite volume method for elliptic boundary value problems. Zbl 1188.65148Erath, Christoph; Praetorius, Dirk 5 2009 Simple a posteriori error estimators for the \(h\)-version of the boundary element method. Zbl 1175.65126Ferraz-Leite, S.; Praetorius, D. 25 2008 Averaging techniques for the a posteriori BEM error control for a hypersingular integral equation in two dimensions. Zbl 1140.65089Carstensen, Carsten; Praetorius, Dirk 17 2007 Averaging techniques for a posteriori error control in finite element and boundary element analysis. Zbl 1298.65161Carstensen, Carsten; Praetorius, Dirk 11 2007 Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. I: Analysis. Zbl 1160.74355Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja 3 2007 Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. II: Numerical simulation. Zbl 1160.74356Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja 3 2007 Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. Zbl 1105.65124Carstensen, Carsten; Praetorius, Dirk 24 2006 \(\mathcal H\)-matrix techniques for stray-field computations in computational micromagnetics. Zbl 1142.78311Popović, Nikola; Praetorius, Dirk 1 2006 Numerical analysis for a macroscopic model in micromagnetics. Zbl 1088.78009Carstensen, Carsten; Praetorius, Dirk 10 2005 Applications of \(\mathcal H\)-matrix techniques in micromagnetics. Zbl 1070.78011Popović, N.; Praetorius, D. 7 2005 Effective simulation of a macroscopic model for stationary micromagnetics. Zbl 1063.78016Carstensen, Carsten; Praetorius, Dirk 6 2005 ...and 7 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 568 Authors 80 Praetorius, Dirk 28 Carstensen, Carsten 27 Feischl, Michael 27 Melenk, Jens Markus 24 Führer, Thomas 21 Karkulik, Michael 16 Gantner, Gregor 13 Erath, Christoph 12 Ruggeri, Michele 11 Faustmann, Markus 10 Heuer, Norbert 10 Stephan, Ernst Peter 9 Aurada, Markus 9 Haberl, Alexander 8 Nochetto, Ricardo Horacio 7 Bespalov, Alexei 7 Di Fratta, Giovanni 7 Ferraz-Leite, Samuel 7 Heid, Pascal 6 Chen, Jingrun 6 Funken, Stefan A. 6 Gimperlein, Heiko 6 Innerberger, Michael 6 Weinmüller, Ewa B. 5 Bringmann, Philipp 5 Giannelli, Carlotta 5 Langer, Ulrich 5 Rieder, Alexander 5 Schimanko, Stefan 5 Stevenson, Rob P. 5 Wihler, Thomas Pascal 4 Becker, Roland 4 Bertrand, Fleurianne 4 Boffi, Daniele 4 Bracco, Cesare 4 Gallistl, Dietmar 4 Gedicke, Joscha 4 Goldenits, Petra 4 Harbrecht, Helmut 4 Jerez-Hanckes, Carlos 4 Ma, Rui 4 Morgenstern, Philipp 4 Page, Marcus 4 Pfeiler, Carl-Martin 4 Schlömerkemper, Anja 4 Vazquez, Rafael 4 Vohralík, Martin 4 Wick, Thomas 4 Xu, Yifeng 3 Atroshchenko, Elena 3 Auzinger, Winfried 3 Banz, Lothar 3 Betcke, Timo 3 Bordas, Stéphane Pierre Alain 3 Buffa, Annalisa 3 Chung, Tsz Shun Eric 3 Dölz, Jürgen 3 Ern, Alexandre 3 Gaddam, Sharat 3 Gudi, Thirupathi 3 Hiptmair, Ralf 3 Koch, Othmar 3 Kreuzer, Christian 3 Kurz, Stefan 3 Leonel, Edson Denner 3 Li, Yuwen 3 März, Roswitha 3 Natarajan, Sundararajan 3 Of, Günther 3 Ortner, Christoph 3 Özdemir, Ceyhun 3 Parvizi, Maryam 3 Peterseim, Daniel 3 Pollock, Sara 3 Popović, Nikola 3 Repin, Sergeĭ Igorevich 3 Rodrigues Neto, Antônio 3 Sayas, Francisco-Javier 3 Schafelner, Andreas 3 Schmidt, Anja 3 Schorr, Robert 3 Schwab, Christoph 3 Stiftner, Bernhard 3 Verani, Marco 3 Wang, Cheng 3 Wu, Jiming 3 Xie, Changjian 3 Zhou, Yanhui 2 An, Rong 2 Angleitner, Niklas 2 Bagherzadeh, Amir Saboor 2 Bakry, Marc 2 Banjai, Lehel 2 Bebendorf, Mario 2 Bonito, Andrea 2 Borthagaray, Juan Pablo 2 Canuto, Claudio 2 Chaillat, Stéphanie 2 Chambolle, Antonin 2 Chaumont-Frelet, Théophile ...and 468 more Authors all top 5 Cited in 83 Serials 48 Computers & Mathematics with Applications 36 Numerische Mathematik 31 SIAM Journal on Numerical Analysis 30 Computer Methods in Applied Mechanics and Engineering 25 Computational Methods in Applied Mathematics 18 Mathematics of Computation 16 Journal of Computational Physics 15 Applied Numerical Mathematics 12 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Journal of Scientific Computing 10 Engineering Analysis with Boundary Elements 9 Journal of Computational and Applied Mathematics 8 SIAM Journal on Scientific Computing 8 Advances in Computational Mathematics 7 M\(^3\)AS. 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