[1] Ole Klein, Olaf A. Cirpka, Peter Bastian, and Olaf Ippisch. Efficient geostatistical inversion of transient groundwater flow using preconditioned nonlinear conjugate gradients. Advances in Water Resources, 102:161 -- 177, 2017. [ bib | DOI | http ]
Keywords: Inverse modeling
[2] M. Piatkowski, S. Müthing, and P. Bastian. A stable and high-order accurate discontinuous galerkin based splitting method for the incompressible navier-stokes equations. arXiv:1612.00657, submitted to Journal of Computational Physics, 2016. [ bib ]
[3] P. Hron, D. Jost, P. Bastian, C. Gallert, J. Winter, and O. Ippisch. Application of reactive transport modeling to growth and transport of microorganisms in the capillary fringe. Vadose Zone Journal, 14(5), 2015. [ bib | DOI | arXiv | http ]
[4] A.Q.T. Ngo, P. Bastian, and O. Ippisch. Numerical solution of steady-state groundwater flow and solute transport problems: Discontinuous galerkin based methods compared to the streamline diffusion approach. Computer Methods in Applied Mechanics and Engineering, 294:331 -- 358, 2015. [ bib | DOI | http ]
[5] H. Remmel, B. Paech, C. Engwer, and P. Bastian. A case study on a quality assurance process for a scientific framework. Computing in Science & Engineering, 16(3):58--66, May 2014. [ bib | DOI ]
[6] Juan Pablo Gallego-Valencia, Johannes Löbbert, Steffen Müthing, Peter Bastian, Christian Klingenberg, and Yinhua Xia. Implementing a discontinuous galerkin method for the compressible, inviscid euler equations in the dune framework. PAMM, 14(1):953--954, 2014. [ bib | DOI | http ]
[7] Peter Bastian. A fully-coupled discontinuous galerkin method for two-phase flow in porous media with discontinuous capillary pressure. Computational Geosciences, 18(5):779--796, 2014. [ bib | DOI | http ]
Keywords: Two-phase flow; Porous medium; Discontinuous Galerkin; Algebraic multigrid; 76S05; 35Q86
[8] Rebecca Neumann, Peter Bastian, and Olaf Ippisch. Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase. Computational Geosciences, 17(1):139--149, 2013. [ bib | DOI ]
Keywords: Two-phase flow; Multicomponent flow; Porous medium; CO2 storage; 76S05; 35Q86
[9] F. Heimann, C. Engwer, O. Ippisch, and P. Bastian. An unfitted interior penalty discontinuous galerkin method for incompressible navier–stokes two-phase flow. International Journal for Numerical Methods in Fluids, 71(3):269--293, 2013. [ bib | DOI | http ]
Keywords: discontinuous Galerkin, unfitted finite elements, Navier–Stokes, two-phase flow, Cartesian cut-cell methods, level set methods
[10] H. Remmel, B. Paech, P. Bastian, and C. Engwer. System testing for scientific software using a regression test environment. Computing in Science and Engineering, 14(2):38--45, 2012. [ bib ]
[11] S. Schlüter, H.-J. Vogel, O. Ippisch, P. Bastian, K. Roth, G. Schenk, H. Schelle, W. Durner, R. Kasteel, and J. Vanderborght. Virtual soils: Assessment of the effects of soil structure on the hydraulic behavior of cultivated soils. Vadose Zone Journal, 11(4), 2012. [ bib | DOI ]
[12] Ronnie L. Schwede, Adrian Ngo, Peter Bastian, Olaf Ippisch, Wei Li, and Olaf A. Cirpka. Efficient parallelization of geostatistical inversion using the quasi-linear approach. Computers & Geosciences, 44(0):78 -- 85, 2012. [ bib | DOI | http ]
Keywords: Parallel computing
[13] Peter Bastian, Markus Blatt, and Robert Scheichl. Algebraic multigrid for discontinuous galerkin discretizations of heterogeneous elliptic problems. Numerical Linear Algebra with Applications, 19(2):367--388, 2012. [ bib | DOI | http ]
Keywords: interior penalty discontinuous Galerkin methods, elliptic PDEs, robustness for heterogeneous coefficients, subspace correction, aggregation-type algebraic multigrid
[14] S. Lang, P. Drouvelis, E. Tafaj, P. Bastian, and B. Sakmann. Fast extraction of neuron morphologies from large-scale sbfsem image stacks. J. Comput Neurosci, 31(3):533--545, 2011. [ bib ]
[15] Peter Bastian, Christian Engwer, Jorrit Fahlke, and Olaf Ippisch. An unfitted discontinuous galerkin method for pore-scale simulations of solute transport. Mathematics and Computers in Simulation, 81(10):2051 -- 2061, 2011. [ bib | DOI | http ]
[16] P. Bastian, F. Heimann, and S. Marnach. Generic implementation of finite element methods in the distributed and unified numerics environment (DUNE). Kybernetika, 46(2):294--315, 2010. [ bib ]
[17] Markus Blatt and Peter Bastian. C++ components describing parallel domain decomposition and communication. International Journal of Parallel, Emergent and Distributed Systems, 24(6):467--477, 2009. [ bib | DOI | .pdf ]
[18] C. Engwer and P. Bastian. An unfitted finite element method using Discontinuous Galerkin. Int. J. Num. Meth. in Engineering, 79(12):1557--1576, 2009. [ bib | DOI | .pdf ]
[19] P. Bastian, A. Chavarria-Krauser, C. Engwer, W. Jäger, S. Marnach, and M. Ptashnyk. Modelling in vitro growth of dense root networks. Journal of Theoretical Biology, 254(1):99--109, 2008. [ bib | DOI | .pdf ]
[20] P. Bastian and M. Blatt. On the generic parallelisation of iterative solvers for the finite element method. Int. J. Computational Science and Engineering, 4(1):56--69, 2008. [ bib | DOI | .pdf ]
[21] P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander. A generic grid interface for parallel and adaptive scientific computing. part II: implementation and tests in DUNE. Computing, 82(2-3):121--138, 2008. [ bib | DOI | .pdf ]
[22] P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, M. Ohlberger, and O. Sander. A generic grid interface for parallel and adaptive scientific computing. part I: abstract framework. Computing, 82(2-3):103--119, 2008. [ bib | DOI | .pdf ]
[23] P. S. Drouvelis, P. Schmelcher, and P. Bastian. Parallel implementation of the recursive Green's function method. Journal of Computational Physics, 215(2):741--756, 2006. arXiv:cond-mat/0507415. [ bib | DOI | .pdf ]
[24] H.-J. Vogel, I. Cousin, O. Ippisch, and P. Bastian. The dominant role of structure for solute transport in soil. experimental evidence and modelling of structure and transport. Hydrol. Earth Syst. Sci., 10(4):495--506, 2006. [ bib | http ]
[25] O. Ippisch, H.-J. Vogel, and P. Bastian. Validity limits for the van genuchten-mualem model and implications for parameter estimation and numerical simulation. Advances in Water Resources, 29(12):1780--1789, 2006. [ bib | DOI ]
[26] P. Bastian and C. Wieners. Multigrid methods on adaptively refined grids. IEEE Computing in Science and Engineering, 8(6):44--54, 2006. [ bib | DOI | .pdf ]
[27] V. Reichenberger, H. Jakobs, P. Bastian, and R. Helmig. A mixed-dimensional finite volume method for multiphase flow in fractured porous media. Adv. Wat. Res., 29(7):1020--1036, 2006. [ bib | DOI | .pdf ]
[28] I. A. Watson, R. S. Crouch, P. Bastian, and S. E. Oswald. Advantages of using adaptive remeshing and parallel computing for modelling biodegradation in groundwater. Adv. Wat. Res., 28(11):1143--1158, 2005. [ bib | DOI ]
[29] T. Neubauer and P. Bastian. On a monotonicity preserving Eulerian-Lagrangian localized adjoint method for advection-diffusion equations. Adv. Wat. Res., 28(12):1292--1309, 2005. [ bib | DOI ]
[30] P. Bastian and S. Lang. Couplex benchmark computations with UG. Computational Geosciences, 8(2):125--147, 2004. [ bib | DOI | .pdf ]
[31] P. Bastian and B. Rivière. Superconvergence and H(div)-projection for discontinuous Galerkin methods. Int. J. Numer. Meth. Fluids., 42(10):1043--1057, 2003. [ bib | DOI | .pdf ]
[32] H. Class, R. Helmig, and P. Bastian. Numerical simulation of non-isothermal multiphase multicomponent processes in porous media. 1. An efficient solution technique. Adv. Wat. Res., 25(5):533--550, 2002. [ bib | DOI | .pdf ]
[33] P. Bastian and R. Helmig. Efficient fully-coupled solution techniques for two-phase flow in porous media. Parallel multigrid solution and large scale computations. Adv. Water Res., 23:199--216, 1999. [ bib | DOI | .pdf ]
[34] P. Bastian, W. Hackbusch, and G. Wittum. Additive and multiplicative multigrid -- a comparison. Computing, 60:345--368, 1998. [ bib | DOI | .pdf ]
[35] R. Helmig, H. Class, R. Huber, H. Sheta, J. Ewing, R. Hinkelmann, H. Jakobs, and P. Bastian. Architecture of the modular program system MUFTE--UG for simulating multiphase flow and transport processes in heterogeneous porous media. Mathematische Geologie, 1998. Band 2. [ bib ]
[36] P. Bastian. Load balancing for adaptive multigrid methods. SIAM J. Sci. Stat. Comput., 19(4):1303--1321, 1998. [ bib | DOI | .pdf ]
[37] P. Bastian, K. Eckstein, and S. Lang. Parallel adaptive multigrid methods in plane linear elasticity problems. Numerical Linear Algebra with Applications, 4(3):153 -- 176, 1997. [ bib | .pdf ]
[38] P. Bastian, K. Birken, S. Lang, K. Johannsen, N. Neuß, H. Rentz-Reichert, and C. Wieners. UG: A flexible software toolbox for solving partial differential equations. Computing and Visualization in Science, 1:27--40, 1997. [ bib | DOI | .pdf ]
[39] P. Bastian and G. Horton. Parallelization of robust multigrid methods: Ilu factorization and frequency decomposition method. SIAM J. Sci. Stat. Comput., 12(6):1457--1470, 1991. [ bib | DOI | .pdf ]

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