References
- Alnaes, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E. and Wells, G.N. (2015) The FEniCS project version 1.5. Archive of Numerical Software, 3(100).
- Cao, W., Huang, W. and Russell, R.D. (1999) A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation. SIAM Journal on Scientific Computing, 20(6): 1978–1994.10.1137/S1064827597327656
- Dacorogna, B. and Moser, J. (1990) On a Partial Differential Equation Involving the Jacobian Determinant. In: Annales de l’Institut Henri Poincaré (C) Non Linear Analysis, 7, 1–26. Elsevier.10.1016/s0294-1449(16)30307-9
- Deckelnick, K., Herbert, P.J. and Hinze, M. (2021) A Novel W1;1 Approach to Shape Optimisation with Lipschitz Domains. arXiv preprint arXiv:2103.13857.10.1051/cocv/2021108
- Etling, T., Herzog, R., Loayza, E. and Wachsmuth, G. (2018) First and second order shape optimization based on restricted mesh deformations. arXiv preprint arXiv:1810.10313.
- Friederich, J., Leugering, G. and Steinmann, P. (2014) Adaptive Finite Elements based on Sensitivities for Topological Mesh Changes. Control and Cybernetics, 43(2); 279–306.
- Geuzaine, C. and Remacle, J.-F. (2009) Gmsh: A 3D Finite Element Mesh Generator with Built-In Pre-and Post-Processing Facilities. International Journal for Numerical methods in Engineering, 70(11): 1309–1331.10.1002/nme.2579
- Guillemin, V. and Pollack, A. (2010) Differential Topology, 370. American Mathematical Society.10.1090/chel/370
- Haubner, J., Siebenborn, M. and Ulbrich, M. (2020) A Continuous Perspective on Modeling of Shape Optimal Design Problems. arXiv preprint arXiv:2004.06942.
- Herzog, R. and Loayza-Romero, E. (2020) A Manifold of Planar Triangular Meshes with Complete Riemannian Metric. arXiv preprint arXiv:2012. 05624.
- Lee, J.M. (2009) Manifolds and Differential Geometry. Graduate Studies in Mathematics 107. American Mathematical Society.10.1090/gsm/107
- Logg, A., Mardal, K.-A., Wells, G.N., et al. (2012) Automated Solution of Differential Equations by the Finite Element Method. Springer.10.1007/978-3-642-23099-8
- Luft, D. and Schulz, V. (2021) Pre-Shape Calculus: Foundations and Application to Mesh Quality Optimization. Control and Cybernetics, 50(3); 263–301.10.2478/candc-2021-0019
- Müller, P.M., Kühl, N., Siebenborn, M., Deckelnick, K., Hinze, M. and Rung, T. (2021) A novel p-harmonic descent approach applied to fluid dynamic shape optimization. arXiv preprint arXiv:2103.14735.10.1007/s00158-021-03030-x
- Onyshkevych, S. and Siebenborn, M. (2020) Mesh Quality Preserving Shape Optimization using Nonlinear Extension Operators. arXiv preprint arXiv:2006.04420.10.1007/s10957-021-01837-8
- Savard, G. and Gauvin, J. (1994) The Steepest Descent Direction for the Nonlinear Bilevel Programming Problem. Operations Research Letters, 15(5): 265–272.10.1016/0167-6377(94)90086-8
- Schmidt, S. (2014) A Two Stage CVT/Eikonal Convection Mesh Deformation Approach for Large Nodal Deformations. arXiv preprint arXiv:1411.7663.
- Schulz, V. and Siebenborn, M. (2016) Computational Comparison of Surface Metrics for PDE Constrained Shape Optimization. Computational Methods in Applied Mathematics, 16(3): 485–496.10.1515/cmam-2016-0009
- Schulz, V., Siebenborn, M. and Welker, K. (2016) Efficient PDE Constrained Shape Optimization based on Steklov-Poincaré Type Metrics. SIAM Journal on Optimization, 26(4): 2800–2819.10.1137/15M1029369
- Shewchuk, J.R. (2002) What is a Good Linear Element? Interpolation, Conditioning, Anisotropy, and Quality Measures. Technical Report. University of California at Berkeley, Department of Electrical Engineering and Computer Science. Berkeley, CA.
- Smolentsev, N.K. (2007) Diffeomorphism groups of compact manifolds. Journal of Mathematical Sciences, 146(6): 6213–6312.10.1007/s10958-007-0471-0