Finite element assembly

Logg, Anders; Mardal, Kent‐André; Wells, Garth N.

doi:10.1007/978-3-642-23099-8_6

Cited by 283 publications

(394 citation statements)

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“…All model components are individual opensource modules coded in python and utilizing the FEniCS framework (Alnaes et al, 2015;Logg et al, 2012a). Computations are performed on unstructured meshes (triangles in 2-D (two dimensions) and tetrahedrons in 3-D), which allow for variable mesh size according to local requirements in spatial resolution and geometry complexity.…”

Section: Advection Of Materials Within a Glaciermentioning

confidence: 99%

“…FEniCS is an open-source project designed for automated solution of PDEs by finite element methods (FEM) (https: //fenicsproject.org, Alnaes et al, 2015;Logg et al, 2012a). It includes several components such as DOLFIN (Logg and Wells, 2010;Logg et al, 2012c), FFC (Kirby and Logg, 2006;Logg et al, 2012b;Ølgaard and Wells, 2010) and FIAT (Kirby, 2004(Kirby, , 2012, which enable automatic solution of linear and non-linear problems once the variational forms of the PDEs are expressed in the Unified Form Language (UFL; Alnaes et al, 2014;Alnaes, 2012).…”

Section: Fenics Softwarementioning

confidence: 99%

“…In this manner, the mesh is refined in an area that covers the actual concentration feature and the distance it can possibly be transported within the refinement time step. For 2-D simulations, mesh refinement is implemented entirely in python using the FEniCS software framework (Alnaes et al, 2015;Logg et al, 2012a). A function representing the coordinates (Fig.…”

Section: Mesh Refinementmentioning

confidence: 99%

“…Although dynamics of debris-ice mixtures can differ from clean-ice dynamics depending on several parameters such as concentration of debris, particle size and temperature (Moore, 2014), in this work we assume that sediment inclusions within the glacier do not affect ice rheology due to the small total amount of transported material in comparison to overall ice volume. The model is coded in python and relies on the FEniCS framework, an open-source software for automated solution of partial differential equations (PDEs) (Alnaes et al, 2015;Logg et al, 2012a). The model employs an existing benchmarked full-Stokes ice flow model (icetools; Jarosch, 2008, now implemented in FEniCS) to compute 3-D velocity fields that govern an advection algorithm used to describe debris transport.…”

Section: Introductionmentioning

confidence: 99%

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Modelling debris transport within glaciers by advection in a full-Stokes ice flow model

Wirbel¹,

Jarosch²,

Nicholson³

2018

The Cryosphere

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Abstract. Glaciers with extensive surface debris cover respond differently to climate forcing than those without supraglacial debris. In order to include debris-covered glaciers in projections of glaciogenic runoff and sea level rise and to understand the paleoclimate proxy recorded by such glaciers, it is necessary to understand the manner and timescales over which a supraglacial debris cover develops. Because debris is delivered to the glacier by processes that are heterogeneous in space and time, and these debris inclusions are altered during englacial transport through the glacier system, correctly determining where, when and how much debris is delivered to the glacier surface requires knowledge of englacial transport pathways and deformation. To achieve this, we present a model of englacial debris transport in which we couple an advection scheme to a full-Stokes ice flow model. The model performs well in numerical benchmark tests, and we present both 2-D and 3-D glacier test cases that, for a set of prescribed debris inputs, reproduce the englacial features, deformation thereof and patterns of surface emergence predicted by theory and observations of structural glaciology. In a future step, coupling this model to (i) a debris-aware surface mass balance scheme and (ii) a supraglacial debris transport scheme will enable the co-evolution of debris cover and glacier geometry to be modelled.

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Section: Advection Of Materials Within a Glaciermentioning

confidence: 99%

Section: Fenics Softwarementioning

confidence: 99%

Section: Mesh Refinementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling debris transport within glaciers by advection in a full-Stokes ice flow model

Wirbel¹,

Jarosch²,

Nicholson³

2018

The Cryosphere

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“…O desenvolvimento do código computacional de elementos finitos utiliza as ferramentas disponíveis em FEniCS [7]. A disponibilidade de integração com ferramentas computacionais de alto nível torna possível a integração com softwares de georreferenciamento, manipulação e processamento das soluções para adequada análise e apresentação.…”

Section: Desenvolvimento E Modelo Conceitualunclassified

Transporte de Contaminantes em Aquífero Freático

Santos¹,

Jesus²,

Wendland³

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. A resolução numérica da equação do transporte de contaminantes com campo de velocidades determinado pela solução da equação não linear do modelo de fluxo deágua subterrânea em aquífero freáticoé apresentada. Neste trabalho, uma estimativa inicial para o método iterativo de Picard aplicadoà equação do fluxoé determinado com base nas cargas hidráulicas dos poços de monitoramento e, em seguida, o campo de velocidades gerado em aquífero livre com poço de bombeamento e recargaé transferido para a equação de advecção-difusão-reação que determina uma distribuição de contaminantes no domínio. Palavras-chave. Aquífero Livre, Nível Freático, Método de Elementos Finitos, FEniCS IntroduçãoA compreensão dos fenômenos hídricos que descrevem a migração de poluentes em meio poroso saturado requer uma combinação de soluções numéricas. Ou seja,é preciso que o modelo matemático que descreve o comportamento hidráulico do aquífero esteja acopladoàs equações do transporte de contaminantes através do campo de velocidades do fluxo subterrâneo. Assim, a solução do fluxo fornece a distribuição de cargas hidráulicas e um campo de velocidades, após ser obtido pela Lei de Darcy,é implementado no problema do transporte para a definição de suas componentes dispersivas e advectivas.Neste trabalho, a simulação computacional considera que o fluxo subterrâneo ocorre em aquífero livre de domínio retangular e que o nível freático sofre alterações devido as vazões constantes em poços penetrantes no seu interior. Desta forma, a solução numérica das equações não lineares de Boussinesq requer a implementação do esquema de iterações de Picard. O artigo tem como objetivo obter o campo de velocidades deáguas subterrâneas em aquífero livre para implementação na resolução adaptativa do problema de transporte de contaminantes. Assim, o texto foi organizado visando atender os três passos principais da modelagem dos recursos hídricos [2]: i.) desenvolvimento e modelo conceitual, ii.)

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Uplift histories of Africa and Australia from linear inverse modeling of drainage inventories

et al. 2015

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We describe and apply a linear inverse model which calculates spatial and temporal patterns of uplift rate by minimizing the misfit between inventories of observed and predicted longitudinal river profiles. Our approach builds upon a more general, nonlinear, optimization model, which suggests that shapes of river profiles are dominantly controlled by upstream advection of kinematic waves of incision produced by spatial and temporal changes in regional uplift rate. Here we use the method of characteristics to solve a version of this problem. A damped, nonnegative, least squares approach is developed that permits river profiles to be inverted as a function of uplift rate. An important benefit of a linearized treatment is low computational cost. We have tested our algorithm by inverting 957 river profiles from both Africa and Australia. For each continent, the drainage network was constructed from a digital elevation model. The fidelity of river profiles extracted from this network was carefully checked using satellite imagery. River profiles were inverted many times to systematically investigate the trade-off between model misfit and smoothness. Spatial and temporal patterns of both uplift rate and cumulative uplift were calibrated using independent geologic and geophysical observations. Uplift patterns suggest that the topography of Africa and Australia grew in Cenozoic times. Inverse modeling of large inventories of river profiles demonstrates that drainage networks contain coherent signals that record the regional growth of elevation.

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Finite element assembly

Cited by 283 publications

References 0 publications

Modelling debris transport within glaciers by advection in a full-Stokes ice flow model

Modelling debris transport within glaciers by advection in a full-Stokes ice flow model

Transporte de Contaminantes em Aquífero Freático

Uplift histories of Africa and Australia from linear inverse modeling of drainage inventories

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