An Object Oriented Parallel Finite Element Scheme for Computations of PDEs: Design and Implementation

Ganesan, Sashikumaar; John, Volker; Matthies, Gunar; Meesala, Raviteja; Abdus, Shamim; Wilbrandt, Ulrich

doi:10.1109/hipcw.2016.023

Cited by 19 publications

(19 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a part of future work, a number of steps can be performed to make the computations faster. These include parallelizing the solver [37] and multikernel learning [38]. Future works also include generating the decentralized law based on the dynamical behavior of fluid particles for the purpose of computational efficiency.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Partial Differential Equation-Based Trajectory Planning for Multiple Unmanned Air Vehicles in Dynamic and Uncertain Environments

Radmanesh

Kumar

French

2020

Journal of Dynamic Systems, Measurement, and Control

View full text Add to dashboard Cite

This paper proposes a physics-inspired method for unmanned aerial vehicle (UAV) trajectory planning in three dimensions using partial differential equations (PDEs) for application in dynamic hostile environments. The proposed method exploits the dynamical property of fluid flowing through a porous medium. This method evaluates risk to generate porosity values throughout the computational domain. The trajectory that encounters the highest porosity values determines the trajectory from the point of origin to the goal position. The best trajectory is found using the reaction of the fluid in porous media by the way of streamlines obtained by numerically solving the PDEs representing the fluid flow. Constraints due to UAV dynamics, obstacles, and predefined way points are applied to the problem after solving for the best trajectory to find the optimal and feasible trajectory. This method shows near-optimality and much reduced computational effort when compared to the other typical numerical optimization methods.

show abstract

Section: Resultsmentioning

confidence: 99%

“…The geographical area of the study is Sevilleta National Wildlife Refuge, Albuquerque, NM. The trajectory has been generated by cost functions (36) and (37) have been shown in Fig. 7 by white and black color, respectively.…”

Section: Three-dimensionalmentioning

confidence: 99%

Partial Differential Equation-Based Trajectory Planning for Multiple Unmanned Air Vehicles in Dynamic and Uncertain Environments

Radmanesh

Kumar

French

2020

Journal of Dynamic Systems, Measurement, and Control

View full text Add to dashboard Cite

show abstract

“…The computed results are visualized with the software package ParaView [1,6] that does not require global numbers for the d.o.f.s. However, if needed, global numbers for d.o.f.s across all processes can be assigned, compare [18]. Altogether, the used concepts turned out to be applicable in the same way for the sequential as well as for the parallel code.…”

Section: Mapped Finite Element Spacesmentioning

confidence: 98%

“…Certain master types match with certain slave types, see Ta- The communication structure is stored in a class called ParFEMapper, while the communication itself is performed by a class named ParFECommunicator. Setting up the ParFEMapper and ParFECommunicator requires some communication itself, and a detailed description of this task is presented in [18]. In what follows, only an overview of it is given, including a short description of those data fields of ParFEMapper that are relevant when updating the d.o.f.s of a certain master-slave relation, see Table 1.…”

Section: Organizing Communicationmentioning

confidence: 99%

ParMooN—A modernized program package based on mapped finite elements

Wilbrandt

Bartsch

Ahmed

et al. 2017

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

ParMooN is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor MooNMD [28]: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierar- * Corresponding author.Email addresses: ulrich.wilbrandt@wias-berlin.de (Ulrich Wilbrandt), clemens.bartsch@wias-berlin.de (Clemens Bartsch), naveed.ahmed@wias-berlin.de (Naveed Ahmed), najib.alia@wias-berlin.de (Najib Alia), felix.anker@wias-berlin.de (Felix Anker), laura.blank@wias-berlin.de (Laura Blank), alfonso.caiazzo@wias-berlin.de (Alfonso Caiazzo), sashi@cds.iisc.ac.in (Sashikumaar Ganesan), swetlana.giere@wias-berlin.de (Swetlana Giere), gunar.matthies@tu-dresden.de (Gunar Matthies), raviteja@cmg.cds.iisc.ac.in (Raviteja Meesala), shamim@cmg.cds.iisc.ac.in (Abdus Shamim), jagan@cmg.cds.iisc.ac.in (Jagannath Venkatesan), volker.john@wias-berlin.de (Volker John)1 The work of Najib Alia has been supported by a funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 675715 (MIMESIS).2 The work of Felix Anker has been supported by grant Jo329/10-2 within the DFG priority programme 1679: Dynamic simulation of interconnected solids processes.3 The work of Sashikumaar Ganesan has partially been supported by the Naval Research Board, DRDO, India through the grant NRB/4003/PG/368. 4 The work of Volker John has partially been supported by grant Jo329/10-2 within the DFG priority programme 1679: Dynamic simulation of interconnected solids processes. chy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of ParMooN. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library PETSc. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.

show abstract

“…The finite element library ParMooN has been used and validated in several publications [45,101], including fluid flow in porous media [99]. The scope of this section is to assess the finite element solver and the accuracy of the immersed boundary method considering a setting particularly relevant for the problem of interest.…”

Section: Validation and Benchmarking Of The Numerical Solvermentioning

confidence: 99%

Modeling, simulation, and optimization of geothermal energy production from hot sedimentary aquifers

et al. 2020

Self Cite

View full text Add to dashboard Cite

Geothermal district heating development has been gaining momentum in Europe with numerous deep geothermal installations and projects currently under development. With the increasing density of geothermal wells, questions related to the optimal and sustainable reservoir exploitation become more and more important. A quantitative understanding of the complex thermo-hydraulic interaction between tightly deployed geothermal wells in heterogeneous temperature and permeability fields is key for a maximum sustainable use of geothermal resources. Motivated by the geological settings of the Upper Jurassic aquifer in the Greater Munich region, we develop a computational model based on finite element analysis and gradient-free optimization to simulate groundwater flow and heat transport in hot sedimentary aquifers, and numerically investigate the optimal positioning and spacing of multi-well systems. Based on our numerical simulations, net energy production from deep geothermal reservoirs in sedimentary basins by smart geothermal multi-well arrangements provides significant amounts of energy to meet heat demand in highly urbanized regions. Our results show that taking into account heterogeneous permeability structures and a variable reservoir temperature may drastically affect the results in the optimal configuration. We demonstrate that the proposed numerical framework is able to efficiently handle generic geometrical and geological configurations, and can be thus flexibly used in the context of multi-variable optimization problems. Hence, this numerical framework can be used to assess the extractable geothermal energy from heterogeneous deep geothermal reservoirs by the optimized deployment of smart multi-well systems. Keywords Porous and fractured geothermal reservoir modeling • Geothermal multi-well configurations • Finite element method • Thermo-hydraulic coupling • Optimization • Open-source software PACS 65M60 • 76S05 • 86-08 • 86A20 Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

show abstract

An Object Oriented Parallel Finite Element Scheme for Computations of PDEs: Design and Implementation

Cited by 19 publications

References 12 publications

Partial Differential Equation-Based Trajectory Planning for Multiple Unmanned Air Vehicles in Dynamic and Uncertain Environments

Partial Differential Equation-Based Trajectory Planning for Multiple Unmanned Air Vehicles in Dynamic and Uncertain Environments

ParMooN—A modernized program package based on mapped finite elements

Modeling, simulation, and optimization of geothermal energy production from hot sedimentary aquifers

Contact Info

Product

Resources

About