Gitterbasierte Numerische Verfahren
- dune-gdt: generische Diskretisierungs toolbox
- dune-xt: Erweiterungen für DUNE
- dune-fem-dg: Discontinuous Galerkin Methoden
Modellreduktion
pyMOR
pyMOR - Model Order Reduction with Python - is a software library for building model order reduction applications with the Python programming language. Its main focus lies on the application of reduced basis methods to parameterized partial differential equations. All algorithms in pyMOR are formulated in terms of abstract interfaces for seamless integration with external high-dimensional PDE solvers. Moreover, pure Python implementations of finite element and finite volume discretizations using the NumPy/SciPy scientific computing stack are provided for getting started quickly.
Mehr Informationen finden SIe auf der offiziellen Homepage.
Entwickler:
Publikationen:
- Milk R, Rave S, Schindler F. 2016. ‘pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, Nr. 5: 194-216. doi: 10.1137/15M1026614.
emgr
\[\color{#00568a}{\huge{\text{em}}}\color{#e88e3f}{\huge{\text{gr}}}\] emgr - the Empirical Gramian framework for model reduction of input-output systems. Empirical gramians can be computed for linear and nonlinear state-space control systems for purposes of model order reduction (MOR), system identification (SYSID) and uncertainty quantification (UQ). Model reduction using empirical gramians can be applied to the state-space, to the parameter-space or both through combined reduction. For state reduction, balanced truncation of the empirical controllability gramian and the empirical observability gramian, or alternatively, direct truncation (approximate balancing) of the empirical cross gramian (or the empirical linear cross gramian for large-scale linear systems) is available. For parameter reduction, parameter identification and sensitivity analysis the empirical sensitivity gramian (controllability of parameters) or the empirical identifiability gramian (observability of parameters) are provided. Combined state and parameter reduction is enabled by the empirical joint gramian, which computes controllability and observability of states (cross gramian) and observability of parameters (cross-identifiability gramian) concurrently. The empirical gramian framework -
emgr
is a compact open-source toolbox for (empirical) GRAMIAN-based model reduction and compatible with OCTAVE and MATLAB.emgr
provides a common interface for the computation of empirical gramians and empirical covariance matrices.Mehr Informationen finden SIe auf der offizielle Homepage.
Entwickler:
Publikationen:
- C. Himpe; 'emgr -- the Empirical Gramian Framework'; Algorithms, 11(7): 91, 2018. https://doi.org/10.3390/a11070091
Gitterbasierte Numerische Verfahren
dune-gdt
\[\color{#00568a}{\large{\text{dune-}}}\color{#e88e3f}{\large{\text{gdt}}}\]
dune-gdt is a DUNE module which provides a generic discretization toolbox for grid-based numerical methods. It contains building blocks - like local operators, local evaluations, local assemblers - for discretization methods as well as generic interfaces for objects like discrete function spaces and basefunction sets. Implementations are provided using the main DUNE discretization modules, like dune-fem, dune-functions and dune-pdelab.
Mehr Informationen finden SIe auf der offizielle Homepage.
Entwickler:
dune-xt
\[\color{#00568a}{\huge{\text{dune-}}}\color{#e88e3f}{\huge{\text{xt}}}\] The dune eXTensions project aims to provide an extra layer of usability and convenience to existing DUNE modules and at the same time to enable programming of generic algorithms, in particular in the context of discretization frameworks. It consists of the four modules dune-xt-common, dune-xt-grid, dune-xt-functions and dune-xt-la.
Mehr Informationen finden Sie auf den Seiten der github.com/dune-community oder des jeweiligen DUNE Moduls.
Entwickler:
Publikationen:
- . . ‘Extending DUNE: The dune-xt modules.’ Archive of Numerical Software 5, Nr. 1: 193-216. doi: 10.11588/ans.2017.1.27720.
dune-fem-dg
\[\color{#00568a}{\huge{\text{dune-}}}\color{#e88e3f}{\huge{\text{fem-dg}}}\] This module provides highly efficient implementations of the Discontinuous Galerkin (DG) method for solving a wide range of non linear partial differential equations (PDE). The interfaces used are highly flexible and customizable, providing for example mechanisms for using distributed parallelization, local grid adaptivity with dynamic load balancing, and check pointing.
Mehr Informationen finden Sie auf der gitlab.dune-project.org/dune-fem/dune-fem-dg Homepage.
Entwickler:
- Stefan Girke
- Robert Klöfkorn
- Tobias Malkmus
- ...
Publikationen:
- . . ‘The DUNE-FEM-DG module.’ Archive of Numerical Software 5, Nr. 1: 21--61. doi: 10.11588/ans.2017.1.28602.