Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media

In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het- erogeneous media. Our approach uses the technique of multilevel methods and the recently proposed preconditioner based on additive Schur complement approximation by J. Kraus (see [8]). The main results are the design and a theoretical and numerical justification of an iterative method for such problems that is robust with respect to the contrast of the media, defined as the ratio between the maximum and minimum values of the coefficient (related to the permeability/conductivity).Comment: 28 page

The Finite Element Sea Ice-Ocean Model (FESOM) v.1.4: formulation of an ocean general circulation model

The Finite Element Sea Ice-Ocean Model (FESOM) is the first global ocean general circulation model based on unstructured-mesh methods that has been developed for the purpose of climate research. The advantage of unstructured-mesh models is their flexible multi-resolution modelling functionality. In this study, an overview of the main features of FESOM will be given; based on sensitivity experiments a number of specific parameter choices will be explained; and directions of future developments will be outlined. It is argued that FESOM is sufficiently mature to explore the benefits of multi-resolution climate modelling and that its applications will provide information useful for the advancement of climate modelling on unstructured meshes

Mimetic Coastal Ocean Modeling In General Coordinates And Using Machine Learning Based Predictions

Nonlinear internal waves are a ubiquitous and fundamental aspect of the coastal ecosystem understanding. However, they rely on extreme geographical conditions and precise dimensional equilibrium to be captured accurately. The General Curvilinear Coastal Ocean Model (GCCOM) was validated, serial and parallel versions for a set of experiments showcasing stratified and non-hydrostatic flow phenomena. Still, the 3D curvilinear capability has proven to be elusive. We apply cutting-edge numerical methods to improve upon the previously validated GCCOM, elevating it to field-scale capacity. This reformulation of the GCCOM equations uses novel 3D curvilinear mimetic operators, a buoyancy body force, and mimetic upwind and gradient-based momentum equations developed for this work. This model represents the most complete implementation of the 3D curvilinear mimetic operators utilizing the MOLE library or any other mimetic applications in literature to date. Results show it to be more physically accurate and better energy conserving than the validated GCCOM and other similar models, permitting the use of 3D curvilinear grids for arbitrary geometries, parallelizable arbitrary domain decomposition, and order-of-magnitude wider time steps. Additionally, we implement machine learning models to coastal ocean data to predict Dissolved Oxygen (DO) content with supervised methods; results show a Median Absolute Percentage Error (MAPE) of 2-6% for instantaneous indirect readings of DO and 0.18% for five days forecast of DO in coastal areas, using a previously predicted temperature of 1.60% MAPE. Dissolved Oxygen is known to be a critically important component to track in coastal environments but also expensive to measure and almost impossible to model with traditional methods due to high nonlinearity. The ML component of this thesis opens the possibility of high precision indirect estimates of biogeochemical quantities, along with highly accurate time series forecasts and a host of new applications of machine learning to environmental sciences

Modeling of Thermally Aware Carbon Nanotube and Graphene Based Post CMOS VLSI Interconnect

This work studies various emerging reduced dimensional materials for very large-scale integration (VLSI) interconnects. The prime motivation of this work is to find an alternative to the existing Cu-based interconnect for post-CMOS technology nodes with an emphasis on thermal stability. Starting from the material modeling, this work includes material characterization, exploration of electronic properties, vibrational properties and to analyze performance as a VLSI interconnect. Using state of the art density functional theories (DFT) one-dimensional and two-dimensional materials were designed for exploring their electronic structures, transport properties and their circuit behaviors. Primarily carbon nanotube (CNT), graphene and graphene/copper based interconnects were studied in this work. Being reduced dimensional materials the charge carriers in CNT(1-D) and in graphene (2-D) are quantum mechanically confined as a result of this free electron approximation fails to explain their electronic properties. For same reason Drude theory of metals fails to explain electronic transport phenomena. In this work Landauer transport theories using non-equilibrium Green function (NEGF) formalism was used for carrier transport calculation. For phonon transport studies, phenomenological Fourier’s heat diffusion equation was used for longer interconnects. Semi-classical BTE and Landauer transport for phonons were used in cases of ballistic phonon transport regime. After obtaining self-consistent electronic and thermal transport coefficients, an equivalent circuit model is proposed to analyze interconnects’ electrical performances. For material studies, CNTs of different variants were analyzed and compared with existing copper based interconnects and were found to be auspicious contenders with integrational challenges. Although, Cu based interconnect is still outperforming other emerging materials in terms of the energy-delay product (1.72 fJ-ps), considering the electromigration resistance graphene Cu hybrid interconnect proposed in this dissertation performs better. Ten times more electromigration resistance is achievable with the cost of only 30% increase in energy-delay product. This unique property of this proposed interconnect also outperforms other studied alternative materials such as multiwalled CNT, single walled CNT and their bundles

An Anlaysis of Methods for Modeling Advective-Dominated Transport

Finite element modeling of sharp front advective-dispersive-reactive transport is not accurate for highly advective or reactive problems. Two techniques were studied with the goal of accurately modeling these problems: an h-adaptive method that adjusted element lengths, and Petrov-Galerkin upwinding which used weighting functions of higher polynomial order than that of the basis functions. Finite element models were constructed using linear and quadratic basis functions in one spatial dimension. The h-adaptive method was shown to give good results with linear and quadratic basis functions. Petrov-Galerkin upwinding also yielded excellent results. This method was implemented for both classes of basis functions, but was studied only for the linear case. The benefits of Petrov-Galerkin upwinding depend on user defined parameters that regulate the amount of upwinding applied to the solution. Taylor series and Fourier analyses of the finite element truncation error as well as numerical experimentation were performed to define optimal upwinding parameters. Published results by other investigators were reproduced, and an automated method of deriving optimal upwinding parameters was developed. Analysis and operation of the Petrov-Galerkin models indicated that optimal levels of upwinding are a function of the gradient across each element. This observation led to a new upwinding scheme that adjusts the upwinding condition at each element as a function of the local gradient. Significantly better results were obtained with the new method relative to existing Petrov-Galerkin formulations. The utility of this technique will be greatly enhanced when optimal upwinding conditions are described as a function of dimensionless model parameters such as Peclet, Courant, and Damkohler numbers, and the method is generalized to multiple spatial dimensions.Master of Science in Environmental Engineerin

The future of coastal and estuarine modeling: Findings from a workshop

This paper summarizes the findings of a workshop convened in the United States in 2018 to discuss methods in coastal and estuarine modeling and to propose key areas of research and development needed to improve their accuracy and reliability. The focus of this paper is on physical processes, and we provide an overview of the current state-of-the-art based on presentations and discussions at the meeting, which revolved around the four primary themes of parameterizations, numerical methods, in-situ and remote-sensing measurements,and high-performance computing. A primary outcome of the workshop was agreement on the need to reduce subjectivity and improve reproducibility in modeling of physical processes in the coastal ocean. Reduction of subjectivity can be accomplished through development of standards for benchmarks, grid generation, and validation, and reproducibility can be improved through development of standards for input/output, coupling and model nesting, and reporting. Subjectivity can also be reduced through more engagement with the applied mathematics and computer science communities to develop methods for robust parameter estimation anduncertainty quantification. Such engagement could be encouraged through more collaboration between thef orward and inverse modeling communities and integration of more applied math and computer science into oceanography curricula. Another outcome of the workshop was agreement on the need to develop high-resolution models that scale on advanced HPC systems to resolve, rather than parameterize, processes with horizontal scales that range between the depth and the internal Rossby deformation scale. Unsurprisingly,more research is needed on parameterizations of processes at scales smaller than the depth, includingparameterizations for drag (including bottom roughness, bedforms, vegetation and corals), wave breaking, and air–sea interactions under strong wind conditions. Other topics that require significantly more work to better parameterize include nearshore wave modeling, sediment transport modeling, and morphodynamics. Finally, it was agreed that coastal models should be considered as key infrastructure needed to support research, just like laboratory facilities, field instrumentation, and research vessels. This will require a shift in the way proposals related to coastal ocean modeling are reviewed and funded

Prospects for improving the representation of coastal and shelf seas in global ocean models

Accurately representing coastal and shelf seas in global ocean models represents one of the grand challenges of Earth system science. They are regions of immense societal importance through the goods and services they provide, hazards they pose and their role in global-scale processes and cycles, e.g. carbon fluxes and dense water formation. However, they are poorly represented in the current generation of global ocean models. In this contribution, we aim to briefly characterise the problem, and then to identify the important physical processes, and their scales, needed to address this issue in the context of the options available to resolve these scales globally and the evolving computational landscape. We find barotropic and topographic scales are well resolved by the current state-of-the-art model resolutions, e.g. nominal 1∕12°, and still reasonably well resolved at 1∕4°; here, the focus is on process representation. We identify tides, vertical coordinates, river inflows and mixing schemes as four areas where modelling approaches can readily be transferred from regional to global modelling with substantial benefit. In terms of finer-scale processes, we find that a 1∕12° global model resolves the first baroclinic Rossby radius for only  ∼ 8% of regions  < 500m deep, but this increases to  ∼ 70% for a 1∕72° model, so resolving scales globally requires substantially finer resolution than the current state of the art. We quantify the benefit of improved resolution and process representation using 1∕12° global- and basin-scale northern North Atlantic nucleus for a European model of the ocean (NEMO) simulations; the latter includes tides and a k-ε vertical mixing scheme. These are compared with global stratification observations and 19 models from CMIP5. In terms of correlation and basin-wide rms error, the high-resolution models outperform all these CMIP5 models. The model with tides shows improved seasonal cycles compared to the high-resolution model without tides. The benefits of resolution are particularly apparent in eastern boundary upwelling zones. To explore the balance between the size of a globally refined model and that of multiscale modelling options (e.g. finite element, finite volume or a two-way nesting approach), we consider a simple scale analysis and a conceptual grid refining approach. We put this analysis in the context of evolving computer systems, discussing model turnaround time, scalability and resource costs. Using a simple cost model compared to a reference configuration (taken to be a 1∕4° global model in 2011) and the increasing performance of the UK Research Councils' computer facility, we estimate an unstructured mesh multiscale approach, resolving process scales down to 1.5km, would use a comparable share of the computer resource by 2021, the two-way nested multiscale approach by 2022, and a 1∕72° global model by 2026. However, we also note that a 1∕12° global model would not have a comparable computational cost to a 1° global model in 2017 until 2027. Hence, we conclude that for computationally expensive models (e.g. for oceanographic research or operational oceanography), resolving scales to  ∼ 1.5km would be routinely practical in about a decade given substantial effort on numerical and computational development. For complex Earth system models, this extends to about 2 decades, suggesting the focus here needs to be on improved process parameterisation to meet these challenges