scholarly journals Automating Finite Element Methods for Geodynamics via Firedrake

2022 ◽  
Author(s):  
D. Rhodri Davies ◽  
Stephan C. Kramer ◽  
Siavash Ghelichkhan ◽  
Angus Gibson
Keyword(s):  
Finite Element ◽  
Code Generation ◽  
Automated System ◽  
Plate Motion ◽  
Reproducible Research ◽  
Surface Boundary ◽  
Problem Size ◽  
Mantle Dynamics ◽  
Research Software ◽  
Wide Range

Abstract. Firedrake is an automated system for solving partial differential equations using the finite element method. By applying sophisticated performance optimisations through automatic code-generation techniques, it provides a means to create accurate, efficient, flexible, easily extensible, scalable, transparent and reproducible research software, that is ideally suited to simulating a wide-range of problems in geophysical fluid dynamics. Here, we demonstrate the applicability of Firedrake for geodynamical simulation, with a focus on mantle dynamics. The accuracy and efficiency of the approach is confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12288 compute cores, where the problem size and the number of processing cores are simultaneously increased. In addition, Firedrake's flexibility is highlighted via straightforward application to different physical (e.g. complex nonlinear rheologies, compressibility) and geometrical (2-D and 3-D Cartesian and spherical domains) scenarios. Finally, a representative simulation of global mantle convection is examined, which incorporates 230 Myr of plate motion history as a kinematic surface boundary condition, confirming its suitability for addressing research problems at the frontiers of global mantle dynamics research.

scholarly journals GemPy 1.0: open-source stochastic geological modeling and inversion

2019 ◽  
Vol 12 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Miguel de la Varga ◽  
Alexander Schaaf ◽  
Florian Wellmann
Keyword(s):  
Open Source ◽  
Code Generation ◽  
Raw Material ◽  
Reproducible Research ◽  
Geological Modeling ◽  
Fault Surface ◽  
Wide Range ◽  
Geological Models ◽  
Density Values ◽  
Efficient Code

Abstract. The representation of subsurface structures is an essential aspect of a wide variety of geoscientific investigations and applications, ranging from geofluid reservoir studies, over raw material investigations, to geosequestration, as well as many branches of geoscientific research and applications in geological surveys. A wide range of methods exist to generate geological models. However, the powerful methods are behind a paywall in expensive commercial packages. We present here a full open-source geomodeling method, based on an implicit potential-field interpolation approach. The interpolation algorithm is comparable to implementations in commercial packages and capable of constructing complex full 3-D geological models, including fault networks, fault–surface interactions, unconformities and dome structures. This algorithm is implemented in the programming language Python, making use of a highly efficient underlying library for efficient code generation (Theano) that enables a direct execution on GPUs. The functionality can be separated into the core aspects required to generate 3-D geological models and additional assets for advanced scientific investigations. These assets provide the full power behind our approach, as they enable the link to machine-learning and Bayesian inference frameworks and thus a path to stochastic geological modeling and inversions. In addition, we provide methods to analyze model topology and to compute gravity fields on the basis of the geological models and assigned density values. In summary, we provide a basis for open scientific research using geological models, with the aim to foster reproducible research in the field of geomodeling.

scholarly journals GemPy 1.0: open-source stochastic geological modeling and inversion

2018 ◽  
Author(s):  
Miguel de la Varga ◽  
Alexander Schaaf ◽  
Florian Wellmann
Keyword(s):  
Open Source ◽  
Code Generation ◽  
Raw Material ◽  
Reproducible Research ◽  
Geological Modeling ◽  
Fault Surface ◽  
Wide Range ◽  
Geological Models ◽  
Density Values ◽  
Efficient Code

Abstract. The representation of subsurface structures is an essential aspect of a wide variety of geoscientific investigations and applications: ranging from geofluid reservoir studies, over raw material investigations, to geosequestration, as well as many branches of geoscientific research studies and applications in geological surveys. A wide range of methods exists to generate geological models. However, especially the powerful methods are behind a paywall in expensive commercial packages. We present here a full open-source geomodeling method, based on an implicit potential-field interpolation approach. The interpolation algorithm is comparable to implementations in commercial packages and capable of constructing complex full 3-D geological models, including fault networks, fault-surface interactions, unconformities, and dome structures. This algorithm is implemented in the programming language Python, making use of a highly efficient underlying library for efficient code generation (theano) that enables a direct execution on GPU's. The functionality can be separated into the core aspects required to generate 3-D geological models and additional assets for advanced scientific investigations. These assets provide the full power behind our approach, as they enable the link to Machine Learning and Bayesian inference frameworks and thus a path to stochastic geological modeling and inversions. In addition, we provide methods to analyse model topology and to compute gravity fields on the basis of the geological models and assigned density values. In summary, we provide a basis for open scientific research using geological models, with the aim to foster reproducible research in the field of geomodeling.

Nonlinear dynamic behaviour of guy cables in turbulent winds

2001 ◽  
Vol 28 (1) ◽  
pp. 98-110 ◽  
Author(s):  
Bruce F Sparling ◽  
Alan G Davenport
Keyword(s):  
Finite Element ◽  
Dynamic Behaviour ◽  
Aerodynamic Drag ◽  
Numerical Study ◽  
Horizontal Displacement ◽  
Wind Loading ◽  
Second Phase ◽  
Nonlinear Coupling ◽  
Wide Range ◽  
Cable Vibrations

Large amplitude cable vibrations are difficult to predict using linear theory due to the presence of sag in the suspended profile. A numerical study was therefore undertaken to investigate the dynamic behaviour of inclined cables excited by imposed displacements. To model the nonlinear nature of cable response, a time domain finite element approach was adopted using nonlinear catenary cable elements. Two types of horizontal displacement patterns were enforced at the upper end of the guy. In the first phase of the study, harmonic displacement histories with a wide range of forcing frequencies were considered. In the second phase, random enforced displacements were used to simulate the motion of a guyed mast in gusty winds. The influence of aerodynamic drag and damping forces was investigated by performing analyses under still air, steady wind, and turbulent wind conditions. It was found that nonlinear coupling of related harmonic response components was significant at certain critical frequencies, particular when the excitation was harmonic and acted in the plane of the guy. Positive aerodynamic damping was shown to effectively suppress resonant and nonlinear coupling response.Key words: cables, structural dynamics, wind loading, finite element method, nonlinear analysis, guyed towers.

Local Hydrostatic Pressure Test for Cylindrical Vessels

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
H. Al-Gahtani ◽  
A. Khathlan ◽  
M. Sunar ◽  
M. Naffa'a
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrostatic Pressure ◽  
Cylindrical Vessel ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Wide Range ◽  
Pressure Test ◽  
Local Test ◽  
Alternative Test

The juncture of a small cylindrical nozzle to a large cylindrical vessel is very common in the pressure vessel industry. Upon fabrication, it is required that the whole structure is subjected to pressure testing. The test can be expensive as it necessitates pressurizing the whole structure typically having a large volume. Hence, it is proposed to make a “local test,” which is considerably simpler as it involves capping the small nozzle and testing only a relatively small portion of the structure. This paper investigates the accuracy and reliability of such an alternative test, using the finite-element method. Two different finite-element types are used in the study, specifically a shell-based element and a solid-based element. The verification of the finite-element results for two different cases shows that the models used in the study are valid. It also proves that the two element types yield very similar stress results. In addition, the study includes a numerical investigation of more than 40 different nozzle-to-vessel junctures with a wide range of parameters for the nozzle and vessel. The results indicate that the use of cylindrical caps that are slightly larger than the nozzle is not recommended as it produces stresses that are significantly different from those for the original required pressure test. As such, the study provides an estimate of the smallest size of the cap that may be used in the local test to generate stresses that agree with the full test. For most practical geometries, it is shown that the size of the cap needs to be at least 2–30 times larger than that of the nozzle, depending on the geometrical parameters of the juncture.

NOVEL COUPLING CONSTRAINT TECHNIQUE FOR EXPLICIT FINITE ELEMENT ANALYSIS

2004 ◽  
Vol 01 (02) ◽  
pp. 309-328
Author(s):  
R. J. HO ◽  
S. A. MEGUID ◽  
R. G. SAUVÉ
Keyword(s):  
Finite Element ◽  
Current Method ◽  
Explicit Integration ◽  
Rotation Tensor ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Explicit Finite Element Analysis ◽  
Wide Range ◽  
Large Rotations ◽  
Generalized Constraint

This paper presents a unified novel technique for enforcing nonlinear beam-to-shell, beam-to-solid, and shell-to-solid constraints in explicit finite element formulations. The limitations of classical multi-point constraint approaches are examined at length, particularly in the context of explicit solution schemes. Novel formulation of a generalized constraint method that ensures proper element coupling is then presented, and its computer implementation in explicit integration algorithms is discussed. Crucial in this regard is the accurate and efficient representation of finite rotations, accomplished using an incremental rotation tensor. The results of some illustrative test cases show the accuracy and robustness of the newly developed algorithm for a wide range of deformation, including that in which large rotations are encountered. When compared to existing works, the salient features of the current method are in evidence.

Analysis of Thick-Walled Pipeline Elements Operating in Creep Conditions

2015 ◽  
Vol 712 ◽  
pp. 63-68
Author(s):  
Przemysław Osocha ◽  
Bohdan Węglowski
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Creep Test ◽  
Power Plants ◽  
Steam Pressure ◽  
Creep Model ◽  
Creep Process ◽  
Fe Model ◽  
Element Analysis ◽  
Wide Range

In some coal-fired power plants, pipeline elements have worked for over 200 000 hours and increased number of failures is observed. The paper discuses thermal wear processes that take place in those elements and lead to rupture. Mathematical model based on creep test data, and describing creep processes for analyzed material, has been developed. Model has been verified for pipeline operating temperature, lower than tests temperature, basing on Larson-Miller relation. Prepared model has been used for thermal-strength calculations based on a finite element method. Processes taking place inside of element and leading to its failure has been described. Than, basing on prepared mathematical creep model and FE model introduced to Ansys program further researches are made. Analysis of dimensions and shape of pipe junction and its influence on operational element lifetime is presented. In the end multi variable dependence of temperature, steam pressure and element geometry is shown, allowing optimization of process parameters in function of required operational time or maximization of steam parameters. The article presents wide range of methods. The creep test data were recalculated for operational temperature using Larson-Miller parameter. The creep strain were modelled, used equations and their parameters are presented. Analysis of errors were conducted. Geometry of failing pipe junction was introduced to the Ansys program and the finite element analysis of creep process were conducted.

A Calculation Method of Magnetic Anomaly Field Distribution of Ellipsoid with Arbitrary Posture

2021 ◽  
Author(s):  
Song-tong Han ◽  
Bo Zhang ◽  
Xiao-li Rong ◽  
Lei-xiang Bian ◽  
Guo-kai Zhang ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Magnetic Anomaly ◽  
Field Distribution ◽  
Calculation Method ◽  
Gravity Potential ◽  
Anomaly Field ◽  
Finite Element Software ◽  
Wide Range ◽  
Distribution Equation

The ellipsoidal magnetization model has a wide range of application scenarios. For example, in aviation magnetic field prospecting, mineral prospecting, seabed prospecting, and UXO (unexploded ordnance) detection. However, because the existing ellipsoid magnetization formula is relatively complicated, the detection model is usually replaced by a dipole. Such a model increases the error probability and poses a significant challenge for subsequent imaging and pattern recognition. Based on the distribution of ellipsoid gravity potential and magnetic potential, the magnetic anomaly field distribution equation generated by the ellipsoid is deduced by changing the aspect ratio, making the ellipsoid equivalent to a sphere. The result of formula derivation shows that the two magnetic anomaly fields are consistent. This paper uses COMSOL finite element software to model UXO, ellipsoids, and spheres and analyzes magnetic anomalies. The conclusion shows that the ellipsoid model can completely replace the UXO model when the error range of 1nT is satisfied. Finally, we established two sets of ellipsoids and calculated the magnetic anomalous field distributions on different planes using deduction formulas and finite element software. We compared the experimental results and found that the relative error of the two sets of data was within [Formula: see text]‰. Error analysis found that the error distribution is standardized and conforms to the normal distribution. The above mathematical analysis and finite element simulation prove that the calculation method is simple and reliable and provides a magnetic field distribution equation for subsequent UXO inversion.

A Compliant Transmission Mechanism With Intermittent Contacts for Cycle-Doubling

2006 ◽  
Vol 129 (1) ◽  
pp. 114-121 ◽  
Author(s):  
Nilesh D. Mankame ◽  
G. K. Ananthasuresh
Keyword(s):  
Finite Element ◽  
Conceptual Design ◽  
Finite Element Simulations ◽  
Nonlinear Finite Element ◽  
Transmission Mechanism ◽  
Input Frequency ◽  
Length Scales ◽  
Wide Range ◽  
Macro Scale ◽  
Functional Prototype

A novel compliant transmission mechanism that doubles the frequency of a cyclic input is presented in this paper. The compliant cycle-doubler is a contact-aided compliant mechanism that uses intermittent contact between itself and a rigid surface. The conceptual design for the cycle-doubler was obtained using topology optimization in our earlier work. In this paper, a detailed design procedure is presented for developing the topology solution into a functional prototype. The conceptual design obtained from the topology solution did not account for the effects of large displacements, friction, and manufacturing-induced features such as fillet radii. Detailed nonlinear finite element analyses and experimental results from quasi-static tests on a macro-scale prototype are used in this paper to understand the influence of the above factors and to guide the design of the functional prototype. Although the conceptual design is based on the assumption of quasi-static operation, the modified design is shown to work well in a dynamic setting for low operating frequencies via finite element simulations. The cycle-doubler design is a monolithic elastic body that can be manufactured from a variety of materials and over a range of length scales. This makes the design scalable and thus adaptable to a wide range of operating frequencies. Explicit dynamic nonlinear finite element simulations are used to verify the functionality of the design at two different length scales: macro (device footprint of a square of 170mm side) at an input frequency of 7.8Hz; and meso (device footprint of a square of 3.78mm side) at an input frequency of 1kHz.

Incorporating Neural Network Material Models Within Finite Element Analysis for Rheological Behavior Prediction

2006 ◽  
Vol 129 (1) ◽  
pp. 58-65 ◽  
Author(s):  
B. Scott Kessler ◽  
A. Sherif El-Gizawy ◽  
Douglas E. Smith
Keyword(s):  
Finite Element ◽  
Effective Means ◽  
Element Model ◽  
Operating Conditions ◽  
Behavior Prediction ◽  
Element Analysis ◽  
Material Models ◽  
Rheological Models ◽  
Wide Range ◽  
Novel Method

The accuracy of a finite element model for design and analysis of a metal forging operation is limited by the incorporated material model’s ability to predict deformation behavior over a wide range of operating conditions. Current rheological models prove deficient in several respects due to the difficulty in establishing complicated relations between many parameters. More recently, artificial neural networks (ANN) have been suggested as an effective means to overcome these difficulties. To this end, a robust ANN with the ability to determine flow stresses based on strain, strain rate, and temperature is developed and linked with finite element code. Comparisons of this novel method with conventional means are carried out to demonstrate the advantages of this approach.

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