@article{52233,
  abstract     = {{ELDIRK methods are defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge-Kutta</jats:italic> methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes,  e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability.}},
  author       = {{Mahnken, Rolf and Westermann, Hendrik}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}}},
  doi          = {{10.1007/s00466-024-02442-y}},
  year         = {{2024}},
}

@article{53229,
  author       = {{Santos-Arteaga, Francisco J. and Di Caprio, Debora and Tavana, Madjid and Tena, Emilio Cerda}},
  issn         = {{1063-6706}},
  journal      = {{IEEE Transactions on Fuzzy Systems}},
  keywords     = {{Applied Mathematics, Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering}},
  number       = {{2}},
  pages        = {{460--474}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation}}},
  doi          = {{10.1109/tfuzz.2022.3188875}},
  volume       = {{31}},
  year         = {{2023}},
}

@article{45757,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Three prominent low order implicit time integration schemes are the first order implicit Euler-method, the second order trapezoidal rule and the second order Ellsiepen method. Its advantages are stability and comparatively low computational cost, however, they require the solution of a nonlinear system of equations. This paper presents a general approach for the construction of third order Runge–Kutta methods by embedding the above mentioned implicit schemes into the class of ELDIRK-methods. These will be defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge–Kutta</jats:italic> (DIRK) methods, with the consequence, that no additional system of equations must be solved. The main results—valid also for non-linear ordinary differential equations—are as follows: Two extra function calculations are required in order to embed the implicit Euler-method and one extra function calculation is required for the trapezoidal-rule and the Ellsiepen method, in order to obtain the third order properties, respectively. Two numerical examples are concerned with a parachute with viscous damping and a two-dimensional laser beam simulation. Here, we verify the higher order convergence behaviours of the proposed new ELDIRK-methods, and its successful performances for asymptotically exact global error estimation of so-called reversed embedded RK-method are shown.
</jats:p>}},
  author       = {{Mahnken, Rolf}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation}}},
  doi          = {{10.1007/s00466-023-02347-2}},
  year         = {{2023}},
}

@article{29843,
  author       = {{Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
  issn         = {{0890-5401}},
  journal      = {{Information and Computation}},
  keywords     = {{Computational Theory and Mathematics, Computer Science Applications, Information Systems, Theoretical Computer Science}},
  publisher    = {{Elsevier BV}},
  title        = {{{A Discrete and Continuous Study of the Max-Chain-Formation Problem}}},
  doi          = {{10.1016/j.ic.2022.104877}},
  year         = {{2022}},
}

@article{33332,
  author       = {{Bopp, Frederik and Rojas, Jonathan and Revenga, Natalia and Riedl, Hubert and Sbresny, Friedrich and Boos, Katarina and Simmet, Tobias and Ahmadi, Arash and Gershoni, David and Kasprzak, Jacek and Ludwig, Arne and Reitzenstein, Stephan and Wieck, Andreas and Reuter, Dirk and Müller, Kai and Finley, Jonathan J.}},
  issn         = {{2511-9044}},
  journal      = {{Advanced Quantum Technologies}},
  keywords     = {{Electrical and Electronic Engineering, Computational Theory and Mathematics, Condensed Matter Physics, Mathematical Physics, Nuclear and High Energy Physics, Electronic, Optical and Magnetic Materials, Statistical and Nonlinear Physics}},
  publisher    = {{Wiley}},
  title        = {{{Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling}}},
  doi          = {{10.1002/qute.202200049}},
  year         = {{2022}},
}

@article{30655,
  author       = {{Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  number       = {{3}},
  pages        = {{847--863}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua}}},
  doi          = {{10.1007/s00466-021-02117-y}},
  volume       = {{69}},
  year         = {{2022}},
}

@article{34700,
  author       = {{Gharibian, Sevag and Santha, Miklos and Sikora, Jamie and Sundaram, Aarthi and Yirka, Justin}},
  issn         = {{1016-3328}},
  journal      = {{Computational Complexity}},
  keywords     = {{Computational Mathematics, Computational Theory and Mathematics, General Mathematics, Theoretical Computer Science}},
  number       = {{2}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Quantum generalizations of the polynomial hierarchy with applications to QMA(2)}}},
  doi          = {{10.1007/s00037-022-00231-8}},
  volume       = {{31}},
  year         = {{2022}},
}

@article{30907,
  author       = {{Rodriguez, Alfonso and Otero, Andres and Platzner, Marco and De la Torre, Eduardo}},
  issn         = {{0018-9340}},
  journal      = {{IEEE Transactions on Computers}},
  keywords     = {{Computational Theory and Mathematics, Hardware and Architecture, Theoretical Computer Science, Software}},
  pages        = {{1--1}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{Exploiting Hardware-Based Data-Parallel and Multithreading Models for Smart Edge Computing in Reconfigurable FPGAs}}},
  doi          = {{10.1109/tc.2021.3107196}},
  year         = {{2021}},
}

@article{34042,
  author       = {{Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang, Weifan and Zhang, Cun-Quan}},
  issn         = {{0095-8956}},
  journal      = {{Journal of Combinatorial Theory, Series B}},
  keywords     = {{Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Theoretical Computer Science}},
  pages        = {{61--80}},
  publisher    = {{Elsevier BV}},
  title        = {{{Nowhere-zero 3-flows in toroidal graphs}}},
  doi          = {{10.1016/j.jctb.2021.11.001}},
  volume       = {{153}},
  year         = {{2021}},
}

@article{46135,
  author       = {{Schall, Johannes and Deconinck, Marielle and Bart, Nikolai and Florian, Matthias and Helversen, Martin and Dangel, Christian and Schmidt, Ronny and Bremer, Lucas and Bopp, Frederik and Hüllen, Isabell and Gies, Christopher and Reuter, Dirk and Wieck, Andreas D. and Rodt, Sven and Finley, Jonathan J. and Jahnke, Frank and Ludwig, Arne and Reitzenstein, Stephan}},
  issn         = {{2511-9044}},
  journal      = {{Advanced Quantum Technologies}},
  keywords     = {{Electrical and Electronic Engineering, Computational Theory and Mathematics, Condensed Matter Physics, Mathematical Physics, Nuclear and High Energy Physics, Electronic, Optical and Magnetic Materials, Statistical and Nonlinear Physics}},
  number       = {{6}},
  publisher    = {{Wiley}},
  title        = {{{Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography}}},
  doi          = {{10.1002/qute.202100002}},
  volume       = {{4}},
  year         = {{2021}},
}

@article{34845,
  abstract     = {{Computational Galois theory, in particular the problem of computing the Galois group of a given polynomial, is a very old problem. Currently, the best algorithmic solution is Stauduhar’s method. Computationally, one of the key challenges in the application of Stauduhar’s method is to find, for a given pair of groups H<G, a G-relative H-invariant, that is a multivariate polynomial F that is H-invariant, but not G-invariant. While generic, theoretical methods are known to find such F, in general they yield impractical answers. We give a general method for computing invariants of large degree which improves on previous known methods, as well as various special invariants that are derived from the structure of the groups. We then apply our new invariants to the task of computing the Galois groups of polynomials over the rational numbers, resulting in the first practical degree independent algorithm.}},
  author       = {{Fieker, Claus and Klüners, Jürgen}},
  issn         = {{1461-1570}},
  journal      = {{LMS Journal of Computation and Mathematics}},
  keywords     = {{Computational Theory and Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{141--158}},
  publisher    = {{Wiley}},
  title        = {{{Computation of Galois groups of rational polynomials}}},
  doi          = {{10.1112/s1461157013000302}},
  volume       = {{17}},
  year         = {{2014}},
}

@article{42794,
  abstract     = {{We exhibit a practical algorithm for solving the constructive membership problem for discrete free subgroups of rank 2 in PSL₂(R) or SL₂(R). This algorithm, together with methods for checking whether a two-generator subgroup of PSL₂(R) or SL₂(R) is discrete and free, have been implemented in Magma for groups defined over real algebraic number fields.}},
  author       = {{Eick, B. and Kirschmer, Markus and Leedham-Green, C.}},
  issn         = {{1461-1570}},
  journal      = {{LMS Journal of Computation and Mathematics}},
  keywords     = {{Computational Theory and Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{345--359}},
  publisher    = {{Wiley}},
  title        = {{{The constructive membership problem for discrete free subgroups of rank 2 of SL₂(R)}}},
  doi          = {{10.1112/s1461157014000047}},
  volume       = {{17}},
  year         = {{2014}},
}

@article{46266,
  author       = {{Alizadeh, Bijan and Behnam, Payman and Sadeghi-Kohan, Somayeh}},
  issn         = {{0018-9340}},
  journal      = {{IEEE Transactions on Computers}},
  keywords     = {{Computational Theory and Mathematics, Hardware and Architecture, Theoretical Computer Science, Software}},
  pages        = {{1--1}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{A Scalable Formal Debugging Approach with Auto-Correction Capability based on Static Slicing and Dynamic Ranking for RTL Datapath Designs}}},
  doi          = {{10.1109/tc.2014.2329687}},
  year         = {{2014}},
}

@article{42796,
  abstract     = {{We give an enumeration of all positive definite primitive Z-lattices in dimension n ≥ 3 whose genus consists of a single isometry class. This is achieved by using bounds obtained from the Smith–Minkowski–Siegel mass formula to computationally construct the square-free determinant lattices with this property, and then repeatedly calculating pre-images under a mapping first introduced by G. L. Watson.

We hereby complete the classification of single-class genera in dimensions 4 and 5 and correct some mistakes in Watson’s classifications in other dimensions. A list of all single-class primitive Z-lattices has been compiled and incorporated into the Catalogue of Lattices.}},
  author       = {{Lorch, David and Kirschmer, Markus}},
  issn         = {{1461-1570}},
  journal      = {{LMS Journal of Computation and Mathematics}},
  keywords     = {{Computational Theory and Mathematics, General Mathematics}},
  pages        = {{172--186}},
  publisher    = {{Wiley}},
  title        = {{{Single-class genera of positive integral lattices}}},
  doi          = {{10.1112/s1461157013000107}},
  volume       = {{16}},
  year         = {{2013}},
}

@article{45933,
  author       = {{Karátson, J. and Kovács, Balázs}},
  issn         = {{0898-1221}},
  journal      = {{Computers &amp; Mathematics with Applications}},
  keywords     = {{Computational Mathematics, Computational Theory and Mathematics, Modeling and Simulation}},
  number       = {{3}},
  pages        = {{449--459}},
  publisher    = {{Elsevier BV}},
  title        = {{{Variable preconditioning in complex Hilbert space and its application to the nonlinear Schrödinger equation}}},
  doi          = {{10.1016/j.camwa.2012.04.021}},
  volume       = {{65}},
  year         = {{2012}},
}

@article{45431,
  author       = {{Mahnken, Rolf}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  number       = {{5}},
  pages        = {{408--425}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A Newton-Multigrid algrithm for elasto-plastic/viscoplastic problems}}},
  doi          = {{10.1007/bf00350355}},
  volume       = {{15}},
  year         = {{2008}},
}

@article{45423,
  author       = {{Mahnken, Rolf}},
  issn         = {{1069-8299}},
  journal      = {{Communications in Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, Computational Theory and Mathematics, General Engineering, Modeling and Simulation, Software}},
  number       = {{10}},
  pages        = {{745--754}},
  publisher    = {{Wiley}},
  title        = {{{Improved implementation of an algorithm for non-linear isotropic/kinematic hardening in elastoplasticity}}},
  doi          = {{10.1002/(sici)1099-0887(199910)15:10<745::aid-cnm288>3.0.co;2-r}},
  volume       = {{15}},
  year         = {{2002}},
}

@article{45417,
  author       = {{Döbert, C. and Mahnken, Rolf and Stein, E.}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  number       = {{5}},
  pages        = {{456--467}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Numerical simulation of interface debonding with a combined damage/friction constitutive model}}},
  doi          = {{10.1007/s004660050493}},
  volume       = {{25}},
  year         = {{2002}},
}

@article{45427,
  abstract     = {{<jats:p>In this work a gradient‐based optimization method is applied in order to determine material parameters for a viscoplastic model with dynamic yield surface coupled to damage as presented in 1997. To this end a sensitivity analysis consistent with the integration scheme presented previously is performed in a systematic manner, both for strain and stress controlled experiments. The algorithm is tested in two numerical examples: first, simulated data are used, in order to re‐obtain parameters for the case of damage under monotonic loading. In the second example material parameters are obtained based on experimental data for lcf‐testing of an austenetic stainless steel, thus showing a very good agreement with respect to hardening, rate and damage effects.</jats:p>}},
  author       = {{Mahnken, Rolf and Johansson, Magnus and Runesson, Kenneth}},
  issn         = {{0264-4401}},
  journal      = {{Engineering Computations}},
  keywords     = {{Computational Theory and Mathematics, Computer Science Applications, General Engineering, Software}},
  number       = {{7}},
  pages        = {{925--955}},
  publisher    = {{Emerald}},
  title        = {{{Parameter estimation for a viscoplastic damage model using a gradient‐based optimization algorithm}}},
  doi          = {{10.1108/02644409810236920}},
  volume       = {{15}},
  year         = {{2002}},
}

@article{34897,
  abstract     = {{This paper announces the creation of a database for number fields. It describes the contents and the methods of access, indicates the origin of the polynomials, and formulates the aims of this collection of fields.}},
  author       = {{Klüners, Jürgen and Malle, Gunter}},
  issn         = {{1461-1570}},
  journal      = {{LMS Journal of Computation and Mathematics}},
  keywords     = {{Computational Theory and Mathematics, General Mathematics}},
  pages        = {{182--196}},
  publisher    = {{Wiley}},
  title        = {{{A Database for Field Extensions of the Rationals}}},
  doi          = {{10.1112/s1461157000000851}},
  volume       = {{4}},
  year         = {{2001}},
}