Advances Concerning Multiscale Methods and Uncertainty Quantification in EXA-DUNE

Bastian, Peter; Engwer, Christian; Fahlke, Jorrit; Geveler, Markus; Göddeke, Dominik; Iliev, Oleg; Ippisch, Olaf; Milk, René; Möhring, Jan; Müthing, Steffen; Ohlberger, Mario; Ribbrock, Dirk; Turek, Stefan

doi:10.1007/978-3-319-40528-5_2

Cited by 6 publications

(5 citation statements)

References 23 publications

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“…In continuation of the first project phase, we enhanced the assembly of sparse approximate inverses (SPAI), a kind of preconditioner that we had shown to be very effective within the DUNE solver before [26,9]. Concerning the assembly of such matrices we have investigated three strategies regarding their numerical efficacy (that is their quality in approximating A −1 ), the computational complexity of the actual assembly and ultimately, the total efficiency of the amortised assembly combined with all applications during a system solution.…”

Section: Strong Smoothers On the Gpu: Fast Approximate Inverses With mentioning

confidence: 99%

EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications

Bastian

Engwer

Göddeke

et al. 2014

Lecture Notes in Computer Science

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In the E -D project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively parallel architecture. In order to cope with the increased probability of hardware failures, one aim of the project was to add flexible, application-oriented resilience capabilities into the framework. Continuous improvement of the underlying hardwareoriented numerical methods have included GPU-based sparse approximate inverses, matrix-free sum-factorisation for high-order discontinuous Galerkin discretisations as well as partially matrix-free preconditioners. On top of that, additional scalability is facilitated by exploiting massive coarse grained parallelism offered by multiscale and uncertainty quantification methods where we have focused on the adaptive choice of the coarse/fine scale and the overlap region as well as the combination of local reduced basis multiscale methods and the multilevel Monte-Carlo algorithm. Finally, some of the concepts are applied in a land-surface model including subsurface flow and surface runoff.

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Section: Strong Smoothers On the Gpu: Fast Approximate Inverses With mentioning

confidence: 99%

EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications

Bastian

Engwer

Göddeke

et al. 2014

Lecture Notes in Computer Science

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“…This is no longer the case e.g. for an MsFEM for advection-diffusion problems in which the sampling problem uses the skew-symmetrized bilinear form defined in (29). In this case, the numerical corrector χ ε,0,e K does not vanish.…”

Section: Example 19 (Msfem-cr For Diffusion Problems)mentioning

confidence: 99%

“…Common features among various multiscale methods have previously been used to design flexible and efficient software for the implementation of such methods on the DUNE platform [26,27] within the Exa-Dune project [28]. For example, the distribution of local problems over multiple processors and subsequent coupling in a global problem are handled by designated software components [29]. Our work may contribute to the efficient implementation of all MsFEMs covered by our general framework in such a project and similar endeavours yet to come.…”

Section: Other Motivations For the General Frameworkmentioning

confidence: 99%

Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods

Biezemans

Bris

Legoll

et al. 2024

Comptes Rendus. Mécanique

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Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable discretization space, and next perform a Galerkin approximation of the problem on that space. We investigate here how these approaches can be implemented in a non-intrusive way, in order to facilitate their dissemination within industrial codes or non-academic environments. We develop an abstract framework that covers a wide variety of MsFEMs for linear second-order partial differential equations. Non-intrusive MsFEM approaches are developed within the full generality of this framework, which may moreover be beneficial to steering software development and improving the theoretical understanding and analysis of MsFEMs.

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“…A high-level abstraction for the finite element method is provided with Firedrake [44]. The ExaStencils pipeline generally addresses stencil codes and their operations [18,33] and many research works introduce sophisticated schemes for the optimization of stencils [7,9].…”

Section: Domain-specific Languagesmentioning

confidence: 99%

AIMES: Advanced Computation and I/O Methods for Earth-System Simulations

Kunkel

Jumah

Novikova

et al. 2020

Lecture Notes in Computational Science and Engineering

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Dealing with extreme scale earth system models is challenging from the computer science perspective, as the required computing power and storage capacity are steadily increasing. Scientists perform runs with growing resolution or aggregate results from many similar smaller-scale runs with slightly different initial conditions (the so-called ensemble runs). In the fifth Coupled Model Intercomparison Project (CMIP5), the produced datasets require more than three Petabytes of storage and the compute and storage requirements are increasing significantly for CMIP6. Climate scientists across the globe are developing next-generation models based on improved numerical formulation leading to grids that are discretized in alternative forms such as an icosahedral (geodesic) grid. The developers of these models face similar problems in scaling, maintaining and optimizing code. Performance portability and the maintainability of code are key concerns of scientists as, compared to industry projects, model code is continuously revised and extended to incorporate further levels of detail. This leads to a rapidly growing code base that is rarely refactored. However, code modernization is important to maintain productivity

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Advances Concerning Multiscale Methods and Uncertainty Quantification in EXA-DUNE

Cited by 6 publications

References 23 publications

EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications

EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications

Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods

AIMES: Advanced Computation and I/O Methods for Earth-System Simulations

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