Dr. Konrad Simon

@inbook{ef6d4e1030124b6bbbe357a9de814e9d,

title = "An Error-Based Low-Rank Correction for Pressure Schur Complement Preconditioners",

author = "R.S. Beddig and J. Behrens and S.L. Borne and K. Simon",

year = "2023",

doi = "10.1007/978-3-031-45158-4_5",

language = "English",

booktitle = "Lecture Notes in Computational Science and Engineering",

@inbook{2543a80d2a1b4d428a04ffbf58af1cb0,

title = "Massively Parallel Multiscale Simulations of the Feedback of Urban Canopies",

abstract = "Urban canopies consist of buildings and trees that are aligned along a street in the horizontal direction. These canopies in cities and forests modulate the local climate considerably in a complex way. Canopies constitute very fine subgrid features that actually have a significant impact on other components of earth system models but their feedbacks on larger scales are by now represented in rather heuristic ways. The problem in simulating their impact is twofold: First, their local modeling is delicate and, secondly, the numerical modeling of the scale interaction between fine and large scales is complicated since the fine scale structure is global. We will mostly focus on the second aspect.Multiscale finite element methods (MsFEM) in their classical form have been applied to various porous media problems but the situation in climate, and hence flow-dominated regimes is different from porous media applications. In order to study the effect of various parameters like the concentration of pollutants, or the dynamics of the background velocity and of the temperature in the atmospheric boundary layer, a semi-Lagrangian reconstruction based multiscale finite element framework (SLMsR) developed by [1, 2] for passive tracer transport modeled by an advection-diffusion equation with high-contrast oscillatory diffusion is applied.These methods are composed of two parts: a local-in-time semi-Lagrangian offline phase that pre-computes basis functions and an online phase that uses these basis functions to compute the solution on a coarse Eulerian simulation mesh. The overhead of pre-computing the basis functions in each coarse block can further be reduced by parallelization. The online phase is approximately as fast as a low resolution standard FEM but using the modified basis that carries subgrid information still allows to reveal the fine scale features of a highly resolved solution and is therefore accurate. This approach is studied in order to reveal the feedback of processes in the canopy layer on different scales present in climate simulation models and in particular on the atmospheric boundary layer.We will show the results of massively parallel simulations for passive tracer transport in an urban region using the new multiscale approach and compare them to classical approaches.",

author = "Heena Patel and Konrad Simon and J{\"o}rn Behrens",

year = "2021",

month = mar,

day = "3",

doi = "10.5194/egusphere-egu21-2507",

language = "English",

series = "EGU General Assembly ",

booktitle = "EGU General Assembly 2021",

note = "EGU General Assembly 2021 ; Conference date: 19-04-2021 Through 30-04-2021",

@inbook{cd8e7770388e47d3a35ef56307cc9a3e,

title = "Stable Multiscale Discretizations of L2-Differential Complexes",

abstract = "Global simulations over long time scales in climate sciences often require coarse grids due to computational constraints. This leaves dynamically important smaller scales unresolved. Thus the influence of small scale processes has to be taken care of by different means. State-of-the-art dynamical cores represent the influence of subscale processes typically via subscale parametrizations and often employ heuristic coupling of scales. This, however, unfortunately often lacks mathematical consistency. The aim of this work is to improve mathematical consistency of the upscaling process that transfers information from the subgrid to the coarse scales of the dynamical core and to largely extend the idea of adding subgrid correctors to basis functions for scalar and vector valued elements discretizing various function spaces.Discussing prototypically the issue of weighted Hodge decompositions I will show that standard techniques on coarse meshes fail to find good projections in all parts of a modified de Rham complex if rough data is involved and discuss an idea of how to construct multiscale finite element (MsFEM) correctors to scalar and vector valued finite elements and, further, how to construct stable multiscale element pairings using the theory of finite element exterior calculus (FEEC). This can be seen as a meta-framework that contains the construction of standard MsFEMs [Efendiev2009, Graham2012]. Application examples here comprise porous media, elasticity, and fluid flow as well as electromagnetism in fine-scale and high-contrast media. I will provide the necessary theoretical background in homological algebra and differential geometry, and discuss a scalable MPI based implementation technique suitable for large clusters. Several computational examples will be shown. I may, if time permits, discuss some ideas from homogenisation theory to attack the problem of a proof of accuracy.",

author = "Konrad Simon and J{\"o}rn Behrens",

year = "2020",

month = mar,

day = "10",

doi = "10.5194/egusphere-egu2020-14970",

language = "English",

booktitle = "EGU General Assembly 2020",

note = "EGU General Assembly 2020 ; Conference date: 04-05-2020 Through 08-05-2020",

@inbook{065e1c44ea96440f90d9b35721831ec1,

title = "A Semi-Lagrangian Multiscale Framework for Advection-Dominant Problems",

abstract = "We introduce a new parallelizable numerical multiscale method for advection-dominated problems as they often occur in engineering and geosciences. State of the art multiscale simulation methods work well in situations in which stationary and elliptic scenarios prevail but are prone to fail when the model involves dominant lower order terms which is common in applications. We suggest to overcome the associated difficulties through a reconstruction of subgrid variations into a modified basis by solving many independent (local) inverse problems that are constructed in a semi-Lagrangian step. Globally the method looks like a Eulerian method with multiscale stabilized basis. The method is extensible to other types of Galerkin methods, higher dimensions, nonlinear problems and can potentially work with real data. We provide examples inspired by tracer transport in climate systems in one and two dimensions and numerically compare our method to standard methods.",

author = "Konrad Simon and J{\"o}rn Behrens",

year = "2019",

doi = "10.1007/978-3-030-22747-0_30",

language = "English",

isbn = "978-3-030-22746-3",

series = "Lecture Notes in Computer Science",

publisher = "Springer International Publishing",

pages = "393--409",

editor = "Rodrigues, {Jo{\~a}o M. F.} and Cardoso, {Pedro J. S.} and J{\^a}nio Monteiro and Roberto Lam and Krzhizhanovskaya, {Valeria V.} and Lees, {Michael H.} and Dongarra, {Jack J.} and Sloot, {Peter M.A.}",

booktitle = "Computational Science -- ICCS 2019",

address = "Switzerland",

@inbook{f110a0b36a034587beba6353e48aad38,

title = "Comparison of various coupling methods for 1D diffusion equations with a analytical solution of two phase Stefan problem",

abstract = "We implemented loose and tight coupling methods to understand thermal diffusion between ocean and ice by means of a simplified one-dimensional model set-up proposed by Stefan. A Stefan problem is a prototypical two-phase model that can used to model, for example, melting and freezing of water due to the transfer of heat fluxes between the two phases. We discretized heat fluxes using low order derivatives for loose coupling and higher order derivatives for tight coupling while fluxes are computed at the (moving) interface. Compared to a known reference solution the tight coupling method exhibits a lower error when compared to the loose coupling discretization. However, further numerical tests are required to analyze these coupling methods.",

author = "Anusha Sunkisala and Konrad Simon and J{\"o}rn Behrens",

year = "2019",

language = "English",

isbn = "978-84-949194-5-9",

pages = "709–718",

booktitle = "COUPLED VIII : proceedings of the VIII International Conference on Computational Methods for Coupled Problems in Science and Engineering",

publisher = "CIMNE",