83 research outputs found
Block preconditioning for fault/fracture mechanics saddle-point problems
The efficient simulation of fault and fracture mechanics is a key issue in several applications and is attracting a growing
interest by the scientific community. Using a formulation based on Lagrange multipliers, the Jacobian matrix
resulting from the Finite Element discretization of the governing equations has a non-symmetric generalized saddlepoint
structure. In this work, we propose a family of block preconditioners to accelerate the convergence of Krylov
methods for such problems. We critically review possible advantages and difficulties of using various Schur complement
approximations, based on both physical and algebraic considerations. The proposed approaches are tested
in a number of real-world applications, showing their robustness and efficiency also in large-size and ill-conditioned
problems
Analysis of fiber-reinforced concrete: micromechanics, parameter identification, fast solvers
Proceedings of: Third International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2016). Sofia (Bulgaria), October, 6-7, 2016.Ultrascale computing is required for many important applications in chemistry, computational fluid dynamics etc., see an overview in the paper Applications for Ultrascale Computing by M. Mihajlovic et al. published in the International Journal Supercomputing Frontiers and Innovations, Vol 2 (2015). In this abstract we shortly describe an application that involves many aspects described in the above paper - the multiscale material design problem. The problem of interest is analysis of the fiber reinforced concrete and we focus on modelling of stiffness through numerical homogenization and computing local material properties by inverse analysis. Both problems require a repeated solution of large-scale finite element problems up to 200 million degrees of freedom and therefore the importance of HPC and ultrascale computing is evident.The work is supported by COST Action IC1305 project Network for Sustainable Ultrascale Computing and a bilateral project of collaboration between the Institute of Geonics CAS and IICT BAS. Further support is through the projects LD15105 Ultrascale computing in geosciences and LQ1602 IT4Innovations excellence in science supported by the Ministry of Education, Youth and Sports of the Czech Republic
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Reactive Flows in Deformable, Complex Media
Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today
Modelling fracture in heterogeneous materials on HPC systems using a hybrid MPI/Fortran coarray multi-scale CAFE framework
A 3D multi-scale cellular automata finite element (CAFE) framework for modelling fracture in heterogeneous materials is described. The framework is implemented in a hybrid MPI/Fortran coarray code for efficient parallel execution on HPC platforms. Two open source BSD licensed libraries developed by the authors in modern Fortran were used: CGPACK, implementing cellular automata (CA) using Fortran coarrays, and ParaFEM, implementing finite elements (FE) using MPI. The framework implements a two-way concurrent hierarchical information exchange between the structural level (FE) and the microstructure (CA). MPI to coarrays interface and data structures are described. The CAFE framework is used to predict transgranular cleavage propagation in a polycrystalline iron round bar under tension. Novel results enabled by this CAFE framework include simulation of progressive cleavage propagation through individual grains and across grain boundaries, and emergence of a macro-crack from merging of cracks on preferentially oriented cleavage planes in individual crystals. Nearly ideal strong scaling up to at least tens of thousands of cores was demonstrated by CGPACK and by ParaFEM in isolation in prior work on Cray XE6. Cray XC30 and XC40 platforms and CrayPAT profiling were used in this work. Initially the strong scaling limit of hybrid CGPACK/ParaFEM CAFE model was 2000 cores. After replacing all-to-all communication patterns with the nearest neighbour algorithms the strong scaling limit on Cray XC30 was increased to 7000 cores. TAU profiling on non-Cray systems identified deficiencies in Intel Fortran 16 optimisation of remote coarray operations. Finally, coarray synchronisation challenges and opportunities for thread parallelisation in CA are discussed
A new unified arc-length method for damage mechanics problems
The numerical solution of continuum damage mechanics (CDM) problems suffers
from convergence-related challenges during the material softening stage, and
consequently existing iterative solvers are subject to a trade-off between
computational expense and solution accuracy. In this work, we present a novel
unified arc-length (UAL) method, and we derive the formulation of the
analytical tangent matrix and governing system of equations for both local and
non-local gradient damage problems. Unlike existing versions of arc-length
solvers that monolithically scale the external force vector, the proposed
method treats the latter as an independent variable and determines the position
of the system on the equilibrium path based on all the nodal variations of the
external force vector. This approach renders the proposed solver substantially
more efficient and robust than existing solvers used in CDM problems. We
demonstrate the considerable advantages of the proposed algorithm through
several benchmark 1D problems with sharp snap-backs and 2D examples under
various boundary conditions and loading scenarios. The proposed UAL approach
exhibits a superior ability of overcoming critical increments along the
equilibrium path. Moreover, the proposed UAL method is 1-2 orders of magnitude
faster than force-controlled arc-length and monolithic Newton-Raphson solvers
State Of the Art Report in the fields of numerical analysis and scientific computing. Final version as of 16/02/2020 deliverable D4.1 of the HORIZON 2020 project EURAD.: European Joint Programme on Radioactive Waste Management
Document information Project Acronym EURAD Project Title European Joint Programme on Radioactive Waste Management Project Type European Joint Programme (EJP) EC grant agreement No. 847593 Project starting / end date 1 st June 2019-30 May 2024 Work Package No. 4 Work Package Title Development and Improvement Of NUmerical methods and Tools for modelling coupled processes Work Package Acronym DONUT Deliverable No. 4.
Large-scale Finite Element Simulation of Seismic Soil-Pile foundation-Structure Interaction
Ph.DDOCTOR OF PHILOSOPH
GeomInt–Mechanical Integrity of Host Rocks
This open access book summarizes the results of the collaborative project “GeomInt: Geomechanical integrity of host and barrier rocks - experiment, modeling and analysis of discontinuities” within the Program: Geo Research for Sustainability (GEO: N) of the Federal Ministry of Education and Research (BMBF). The use of geosystems as a source of resources, a storage space, for installing underground municipal or traffic infrastructure has become much more intensive and diverse in recent years. Increasing utilization of the geological environment requires careful analyses of the rock–fluid systems as well as assessments of the feasibility, efficiency and environmental impacts of the technologies under consideration. The establishment of safe, economic and ecological operation of underground geosystems requires a comprehensive understanding of the physical, (geo)chemical and microbiological processes on all relevant time and length scales. This understanding can only be deepened on the basis of intensive laboratory and in-situ experiments in conjunction with reliable studies on the modeling and simulation (numerical experiments) of the corresponding multi-physical/chemical processes. The present work provides a unique handbook for experimentalists, modelers, analysts and even decision makers concerning the characterization of various types of host rocks (salt, clay, crystalline formations) for various geotechnical applications
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