TY - JOUR A1 - Grajewski, Matthias A1 - Kleefeld, Andreas T1 - Detecting and approximating decision boundaries in low-dimensional spaces JF - Numerical Algorithms N2 - A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of scattered points along with the corresponding classification algorithm to construct a representation of a decision curve by points with prescribed maximal distance to the true decision curve. Hereby, our algorithm ensures that the representing point set covers the decision curve in its entire extent and features local refinement based on the geometric properties of the decision curve. We demonstrate applications of our method to problems related to the detection of faults, to multi-criteria decision aid and, in combination with Kirsch’s factorization method, to solving an inverse acoustic scattering problem. In all applications we considered in this work, our method requires significantly less pointwise classifications than previously employed algorithms. KW - MCDA KW - Inverse scattering problem KW - Fault approximation KW - Fault detection Y1 - 2023 SN - 1572-9265 N1 - Corresponding author: Matthias Grajewski VL - 93 IS - 4 PB - Springer Science+Business Media CY - Dordrecht ER - TY - JOUR A1 - Rhoden, Imke A1 - Ball, Christopher Stephen A1 - Grajewski, Matthias A1 - Kuckshinrich, Wilhelm T1 - Reverse engineering of stakeholder preferences – A multi-criteria assessment of the German passenger car sector JF - Renewable and Sustainable Energy Reviews N2 - Germany is a frontrunner in setting frameworks for the transition to a low-carbon system. The mobility sector plays a significant role in this shift, affecting different people and groups on multiple levels. Without acceptance from these stakeholders, emission targets are out of reach. This research analyzes how the heterogeneous preferences of various stakeholders align with the transformation of the mobility sector, looking at the extent to which the German transformation paths are supported and where stakeholders are located. Under the research objective of comparing stakeholders' preferences to identify which car segments require additional support for a successful climate transition, a status quo of stakeholders and car performance criteria is the foundation for the analysis. Stakeholders' hidden preferences hinder the derivation of criteria weightings from stakeholders; therefore, a ranking from observed preferences is used. This study's inverse multi-criteria decision analysis means that weightings can be predicted and used together with a recalibrated performance matrix to explore future preferences toward car segments. Results show that stakeholders prefer medium-sized cars, with the trend pointing towards the increased potential for alternative propulsion technologies and electrified vehicles. These insights can guide the improved targeting of policy supporting the energy and mobility transformation. Additionally, the method proposed in this work can fully handle subjective approaches while incorporating a priori information. A software implementation of the proposed method completes this work and is made publicly available. KW - Regionalization KW - Multi-criteria decision analysis KW - Preference assessment KW - E-Mobility KW - Mobility transition Y1 - 2023 U6 - http://dx.doi.org/10.1016/j.rser.2023.113352 SN - 1364-0321 VL - 181 IS - July 2023 SP - Article number: 113352 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Grajewski, Matthias A1 - Köster, Michael A1 - Turek, Stefan T1 - Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context JF - SIAM Journal on Scientific Computing Y1 - 2009 U6 - http://dx.doi.org/10.1137/050639387 VL - 31 IS - 2 SP - 1539 EP - 1557 PB - Society for Industrial and Applied Mathematics CY - Philadelphia, Pa. ER -