@article{KleefeldPieronek2020,
  author    = {Kleefeld, Andreas and Pieronek, J.},
  title     = {Elastic transmission eigenvalues and their computation via the method of fundamental solutions},
  series = {Applicable Analysis},
  volume    = {100},
  journal   = {Applicable Analysis},
  number    = {16},
  publisher = {Taylore \& Francis},
  address   = {London},
  issn      = {1563-504X},
  doi       = {10.1080/00036811.2020.1721473},
  pages     = {3445 -- 3462},
  year      = {2020},
  abstract  = {A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach.},
  language  = {en}
}
@article{BreussKleefeld2020,
  author    = {Breuß, Michael and Kleefeld, Andreas},
  title     = {Implicit monotone difference methods for scalar conservation laws with source terms},
  series = {Acta Mathematica Vietnamica},
  volume    = {45},
  journal   = {Acta Mathematica Vietnamica},
  publisher = {Springer Singapore},
  address   = {Singapore},
  issn      = {2315-4144},
  doi       = {10.1007/s40306-019-00354-1},
  pages     = {709 -- 738},
  year      = {2020},
  abstract  = {In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970-986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.},
  language  = {en}
}
@article{AsanteAsamaniKleefeldWade2020,
  author    = {Asante-Asamani, E.O. and Kleefeld, Andreas and Wade, B.A.},
  title     = {A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting},
  series = {Journal of Computational Physics},
  volume    = {415},
  journal   = {Journal of Computational Physics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2020.109490},
  year      = {2020},
  abstract  = {A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.},
  language  = {en}
}
@incollection{Kleefeld2020,
  author    = {Kleefeld, Andreas},
  title     = {Numerical calculation of interior transmission eigenvalues with mixed boundary conditions},
  series = {Computational and Analytic Methods in Science and Engineering},
  booktitle = {Computational and Analytic Methods in Science and Engineering},
  editor    = {Constanda, Christian},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-030-48185-8 (Hardcover)},
  doi       = {10.1007/978-3-030-48186-5_9},
  pages     = {173 -- 195},
  year      = {2020},
  abstract  = {Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme.},
  language  = {en}
}
@article{MartinVaqueroKleefeld2020,
  author    = {Mart{\´i}n-Vaquero, J. and Kleefeld, Andreas},
  title     = {Solving nonlinear parabolic PDEs in several dimensions: Parallelized ESERK codes},
  series = {Journal of Computational Physics},
  journal   = {Journal of Computational Physics},
  number    = {423},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2020.109771},
  year      = {2020},
  abstract  = {There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost. Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.},
  language  = {en}
}
@article{Kleefeld2021,
  author    = {Kleefeld, Andreas},
  title     = {The hot spots conjecture can be false: some numerical examples},
  series = {Advances in Computational Mathematics},
  volume    = {47},
  journal   = {Advances in Computational Mathematics},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1019-7168},
  doi       = {10.1007/s10444-021-09911-5},
  year      = {2021},
  abstract  = {The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10- 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.},
  language  = {en}
}
@misc{BurgethKleefeldNaegeletal.2020,
  author    = {Burgeth, Bernhard and Kleefeld, Andreas and Naegel, Beno{\^i}t and Perret, Benjamin},
  title     = {Editorial — Special Issue: ISMM 2019},
  series = {Mathematical Morphology - Theory and Applications},
  volume    = {4},
  journal   = {Mathematical Morphology - Theory and Applications},
  number    = {1},
  publisher = {De Gruyter},
  address   = {Warschau},
  issn      = {2353-3390},
  doi       = {10.1515/mathm-2020-0200},
  pages     = {159 -- 161},
  year      = {2020},
  abstract  = {This editorial presents the Special Issue dedicated to the conference ISMM 2019 and summarizes the articles published in this Special Issue.},
  language  = {en}
}
@article{KleefeldZimmermann2022,
  author    = {Kleefeld, Andreas and Zimmermann, M.},
  title     = {Computing Elastic Interior Transmission Eigenvalues},
  series = {Integral Methods in Science and Engineering},
  journal   = {Integral Methods in Science and Engineering},
  editor    = {Constanda, Christian and Bodmann, Bardo E.J. and Harris, Paul J.},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-031-07171-3},
  doi       = {10.1007/978-3-031-07171-3_10},
  pages     = {139 -- 155},
  year      = {2022},
  abstract  = {An alternative method is presented to numerically compute interior elastic transmission eigenvalues for various domains in two dimensions. This is achieved by discretizing the resulting system of boundary integral equations in combination with a nonlinear eigenvalue solver. Numerical results are given to show that this new approach can provide better results than the finite element method when dealing with general domains.},
  language  = {en}
}
@inproceedings{BurgethKleefeldZhangetal.2022,
  author    = {Burgeth, Bernhard and Kleefeld, Andreas and Zhang, Eugene and Zhang, Yue},
  title     = {Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification},
  series = {Discrete Geometry and Mathematical Morphology},
  booktitle = {Discrete Geometry and Mathematical Morphology},
  editor    = {Baudrier, {\´E}tienne and Naegel, Beno{\^i}t and Kr{\"a}henb{\"u}hl, Adrien and Tajine, Mohamed},
  publisher = {Springer},
  address   = {Cham},
  isbn      = {978-3-031-19897-7},
  doi       = {10.1007/978-3-031-19897-7_5},
  pages     = {48 -- 59},
  year      = {2022},
  abstract  = {Fields of asymmetric tensors play an important role in many applications such as medical imaging (diffusion tensor magnetic resonance imaging), physics, and civil engineering (for example Cauchy-Green-deformation tensor, strain tensor with local rotations, etc.). However, such asymmetric tensors are usually symmetrized and then further processed. Using this procedure results in a loss of information. A new method for the processing of asymmetric tensor fields is proposed restricting our attention to tensors of second-order given by a 2x2 array or matrix with real entries. This is achieved by a transformation resulting in Hermitian matrices that have an eigendecomposition similar to symmetric matrices. With this new idea numerical results for real-world data arising from a deformation of an object by external forces are given. It is shown that the asymmetric part indeed contains valuable information.},
  language  = {en}
}
@article{ChwallekNawrathKrastinaetal.2024,
  author    = {Chwallek, Constanze and Nawrath, Lara and Krastina, Anzelika and Bruksle, Ieva},
  title     = {Supportive research on sustainable entrepreneurship and business practices},
  series = {SECA Sustainable Entrepreneurship for Climate Action},
  journal   = {SECA Sustainable Entrepreneurship for Climate Action},
  number    = {3},
  publisher = {Lapland University of Applied Sciences Ltd},
  address   = {Rovaniemi},
  isbn      = {978-952-316-514-4 (pdf)},
  issn      = {2954-1654 (on-line publication)},
  pages     = {67 Seiten},
  year      = {2024},
  language  = {en}
}