scholarly journals Alternating directions parallel hybrid memory iGRM direct solver for non-stationary simulations

2020 ◽  
Vol 21 (4) ◽  
Author(s):  
Maciej Woźniak ◽  
Anna Janina Bukowska
Keyword(s):  
Isogeometric Analysis ◽  
Parallel Machines ◽  
Sparse Matrix ◽  
Computational Cost ◽  
Three Dimensional ◽  
Modern Method ◽  
Basis Functions ◽  
Computational Domain ◽  
Hybrid Memory ◽  
Hybrid Parallelization

The three-dimensional isogeometric analysis (IGA-FEM) is a modern method for simulation. The idea is to utilize B-splines or NURBS basis functions for both computational domain descriptions and the engineering computations. Refined isogeometric analysis (rIGA) employs a mixture of patches of elements with B-spline basis functions, and $C^0$ separators between them. It enables a reduction of the computational cost of direct solvers. Both IGA and rIGA come with challenging sparse matrix structure, that is expensive to generate. In this paper, we show a hybrid parallelization method to reduce the computational cost of the integration phase using hybrid-memory parallel machines. The two-level parallelization includes the partitioning of the computational mesh into sub-domains on the first level (MPI), and loop parallelization on the second level (OpenMP). We show that hybrid parallelization of the integration reduces the contribution of this phase significantly. Thus, alternative algorithms for fast isogeometric integration are not necessary.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

scholarly journals A Numerical Thermal Analysis of the Heating Process of Large Size Forged Ingots

2018 ◽  
Vol 941 ◽  
pp. 2278-2283
Author(s):  
Nima Bohlooli Arkhazloo ◽  
Farzad Bazdidi-Tehrani ◽  
Morin Jean-Benoit ◽  
Mohammad Jahazi
Keyword(s):  
Heat Transfer ◽  
Heat Treatment ◽  
Conjugate Heat Transfer ◽  
Computational Cost ◽  
Three Dimensional ◽  
Temperature Evolution ◽  
Heating Process ◽  
Computational Domain ◽  
Cfd Model ◽  
Large Size

Simulation and analysis of thermal interactions during heat treatment is of great importance for accurate prediction of temperature evolution of work pieces and consequently controlling the final microstructure and mechanical properties of products. In the present study, a three-dimensional CFD model was employed to predict the heating process of large size forged ingots inside an industrial gas-fired heat treatment furnace. One-ninth section of a loaded furnace, including details such as fixing bars and high-momentum cup burners, was employed as the computational domain. The simulations were conducted using the ANSYS-FLUENT commercial CFD package. The k-ε, P-1 and Probability Density Function (PDF) in the non-premix combustion, as low computational cost numerical approaches were employed to simulate the turbulent fluid flow, thermal radiation, combustion and conjugate heat transfer inside the furnace. Temperature measurement at different locations of the forged ingot surfaces were used to validate the transient numerical simulations. Good agreement was obtained between the predictions of the CFD model and the experimental measurements, demonstrating the reliability of the proposed approach and application of the model for process optimization purposes. Detailed analysis of conjugate heat transfer together with the turbulent combustion showed that the temperature evolution of the product was significantly dependant on the furnace geometry and the severity of turbulent flow structures in the furnace.

scholarly journals ISOGEOMETRIC COLLOCATION METHODS

2010 ◽  
Vol 20 (11) ◽  
pp. 2075-2107 ◽  
Author(s):  
F. AURICCHIO ◽  
L. BEIRÃO DA VEIGA ◽  
T. J. R. HUGHES ◽  
A. REALI ◽  
G. SANGALLI
Keyword(s):  
Theoretical Analysis ◽  
Isogeometric Analysis ◽  
Computational Cost ◽  
Basis Functions ◽  
Three Dimensions ◽  
Collocation Methods ◽  
One Dimensional ◽  
Numerical Tests ◽  
Low Computational Cost ◽  
Theoretical Results

We initiate the study of collocation methods for NURBS-based isogeometric analysis. The idea is to connect the superior accuracy and smoothness of NURBS basis functions with the low computational cost of collocation. We develop a one-dimensional theoretical analysis, and perform numerical tests in one, two and three dimensions. The numerical results obtained confirm theoretical results and illustrate the potential of the methodology.

A High-Order Time Domain Discontinuous Galerkin Method with Orthogonal Tetrahedral Basis for Electromagnetic Simulations in 3-D Heterogeneous Conductive Media

2017 ◽  
Vol 21 (4) ◽  
pp. 1065-1089 ◽  
Author(s):  
Jun Yang ◽  
Wei Cai ◽  
Xiaoping Wu
Keyword(s):  
Discontinuous Galerkin ◽  
Time Domain ◽  
Heterogeneous Media ◽  
Underground Structure ◽  
Three Dimensional ◽  
Low Frequency ◽  
Time Discretization ◽  
High Order ◽  
Basis Functions ◽  
Computational Domain

AbstractWe present a high-order discontinuous Galerkin (DG) method for the time domain Maxwell's equations in three-dimensional heterogeneous media. New hierarchical orthonormal basis functions on unstructured tetrahedral meshes are used for spatial discretization while Runge-Kutta methods for time discretization. A uniaxial perfectly matched layer (UPML) is employed to terminate the computational domain. Exponential convergence with respect to the order of the basis functions is observed and large parallel speedup is obtained for a plane-wave scattering model. The rapid decay of the out-going wave in the UPML is shown in a dipole radiation simulation. Moreover, the low frequency electromagnetic fields excited by a horizontal electric dipole (HED) and a vertical magnetic dipole (VMD) over a layered conductive half-space and a high frequency ground penetrating radar (GPR) detection for an underground structure are investigated, showing the high accuracy and broadband simulation capability of the proposed method.

BDDC PRECONDITIONERS FOR ISOGEOMETRIC ANALYSIS

2013 ◽  
Vol 23 (06) ◽  
pp. 1099-1142 ◽  
Author(s):  
L. BEIRÃO DA VEIGA ◽  
D. CHO ◽  
L. F. PAVARINO ◽  
S. SCACCHI
Keyword(s):  
Convergence Rate ◽  
Domain Decomposition ◽  
Elliptic Problem ◽  
Isogeometric Analysis ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Parallel Computers ◽  
Basis Functions ◽  
Polynomial Degree ◽  
Balancing Domain Decomposition

A Balancing Domain Decomposition by Constraints (BDDC) preconditioner for Isogeometric Analysis of scalar elliptic problems is constructed and analyzed by introducing appropriate discrete norms. A main result of this work is the proof that the proposed isogeometric BDDC preconditioner is scalable in the number of subdomains and quasi-optimal in the ratio of subdomain and element sizes. Another main result is the numerical validation of the theoretical convergence rate estimates by carrying out several two- and three-dimensional tests on serial and parallel computers. These numerical experiments also illustrate the preconditioner performance with respect to the polynomial degree and the regularity of the NURBS basis functions, as well as its robustness with respect to discontinuities of the coefficient of the elliptic problem across subdomain boundaries.

Numerical Study of Three Dimensional Effects of Wave Impact on an Oscillating Wave Surge Converter

2015 ◽  
Author(s):  
Yanji Wei ◽  
Frederic Dias
Keyword(s):  
Numerical Study ◽  
Computational Cost ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Diffraction Reflection ◽  
Linear Wave ◽  
Computational Domain ◽  
Wave Impact ◽  
Relaxation Zone ◽  
3D Effects

A CFD model to study the three-dimensional (3D) effects of wave impact on an Oscillating Wave Surge Converter (OWSC) has been demonstrated. Considering the excessive computational cost of CFD models, a relative small computational domain is used here. The velocity at the outside boundary is prescribed based on the classical non-linear wave theory. A relaxation zone is applied to absorb the diffraction/reflection waves by the device to avoid the re-reflection from the outer boundary. This zone is implemented by adding momentum source terms in the N–S equations to blend the near field flow into the far-field wave environment. The simulation of wave interaction with a fixed flap is performed to demonstrate the validity of the relaxation zone. Simulations of wave interaction with an OWSC by various wave conditions (different wave heights and incident angles) are then carried out to understand the 3D effects of the wave impact. The water elevation in the simulation is in agreement with the observations in the experiment. The variation of the pressure distribution indicates that the wave impact is enhanced at the centre of the flap, due to the water re-entry from the sides of the flap into the centre in 3D tests.

scholarly journals Fast Quadrature Techniques for Retarded Potentials Based on TT/QTT Tensor Approximation

2001 ◽  
Vol 11 (3) ◽  
pp. 342-362 ◽  
Author(s):  
Boris Khoromskij ◽  
Stefan Sauter ◽  
Alexander Veit
Keyword(s):  
Substantial Reduction ◽  
Computational Cost ◽  
Three Dimensional ◽  
Unbounded Domains ◽  
Boundary Integral ◽  
Basis Functions ◽  
Quadrature Rules ◽  
Galerkin Approach ◽  
Tensor Approximation ◽  
Element Matrix

AbstractWe consider the Galerkin approach for the numerical solution of retarded boundary integral formulations of the three dimensional wave equation in unbounded domains. Recently smooth and compactly supported basis functions in time were introduced which allow the use of standard quadrature rules in order to compute the entries of the boundary element matrix. In this paper, we use TT and QTT tensor approximations to increase the efficiency of these quadrature rules. Various numerical experiments show the substantial reduction of the computational cost that is needed to obtain accurate approximations for the arising integrals.

scholarly journals An Online Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Fractured Media

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1382
Author(s):  
Denis Spiridonov ◽  
Maria Vasilyeva ◽  
Aleksei Tyrylgin ◽  
Eric T. Chung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Reduction ◽  
Basis Functions ◽  
Computational Domain ◽  
Filtration Problem ◽  
Spectral Problems ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Element Method

In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow problem in unsaturated soils is described by the Richards equation. To approximate fractures we use the Discrete Fracture Model (DFM). Complex geometric features of the computational domain requires the construction of a fine grid that explicitly resolves the heterogeneities such as fractures. This approach leads to systems with a large number of unknowns, which require large computational costs. In order to develop a more efficient numerical scheme, we propose a model reduction procedure based on the Generalized Multiscale Finite element method (GMsFEM). The GMsFEM allows solving such problems on a very coarse grid using basis functions that can capture heterogeneities. In the GMsFEM, there are offline and online stages. In the offline stage, we construct snapshot spaces and solve local spectral problems to obtain multiscale basis functions. These spectral problems are defined in the snapshot space in each local domain. To improve the accuracy of the method, we add online basis functions in the online stage. The construction of the online basis functions is based on the local residuals. The use of online bases will allow us to get a significant improvement in the accuracy of the method. We present results with different number of offline and online multisacle basis functions. We compare all results with reference solution. Our results show that the proposed method is able to achieve high accuracy with a small computational cost.

scholarly journals The ICON Single-Column Mode

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 906
Author(s):  
Ivan Bašták Ďurán ◽  
Martin Köhler ◽  
Astrid Eichhorn-Müller ◽  
Vera Maurer ◽  
Juerg Schmidli ◽  
...  
Keyword(s):  
Data Storage ◽  
Model Development ◽  
Computational Cost ◽  
Three Dimensional ◽  
Shallow Convection ◽  
Modeling Framework ◽  
Additional Tool ◽  
Eddy Simulation ◽  
Single Column ◽  
Stratocumulus Clouds

The single-column mode (SCM) of the ICON (ICOsahedral Nonhydrostatic) modeling framework is presented. The primary purpose of the ICON SCM is to use it as a tool for research, model evaluation and development. Thanks to the simplified geometry of the ICON SCM, various aspects of the ICON model, in particular the model physics, can be studied in a well-controlled environment. Additionally, the ICON SCM has a reduced computational cost and a low data storage demand. The ICON SCM can be utilized for idealized cases—several well-established cases are already included—or for semi-realistic cases based on analyses or model forecasts. As the case setup is defined by a single NetCDF file, new cases can be prepared easily by the modification of this file. We demonstrate the usage of the ICON SCM for different idealized cases such as shallow convection, stratocumulus clouds, and radiative transfer. Additionally, the ICON SCM is tested for a semi-realistic case together with an equivalent three-dimensional setup and the large eddy simulation mode of ICON. Such consistent comparisons across the hierarchy of ICON configurations are very helpful for model development. The ICON SCM will be implemented into the operational ICON model and will serve as an additional tool for advancing the development of the ICON model.

scholarly journals Retinal vessel segmentation with constrained-based nonnegative matrix factorization and 3D modified attention U-Net

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yang Yu ◽  
Hongqing Zhu
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Computational Cost ◽  
Three Dimensional ◽  
Nonnegative Matrix ◽  
Retinal Vessel ◽  
Classification Problem ◽  
Image Resolution ◽  
Retinal Vessels ◽  
Segmentation Task

AbstractDue to the complex morphology and characteristic of retinal vessels, it remains challenging for most of the existing algorithms to accurately detect them. This paper proposes a supervised retinal vessels extraction scheme using constrained-based nonnegative matrix factorization (NMF) and three dimensional (3D) modified attention U-Net architecture. The proposed method detects the retinal vessels by three major steps. First, we perform Gaussian filter and gamma correction on the green channel of retinal images to suppress background noise and adjust the contrast of images. Then, the study develops a new within-class and between-class constrained NMF algorithm to extract neighborhood feature information of every pixel and reduce feature data dimension. By using these constraints, the method can effectively gather similar features within-class and discriminate features between-class to improve feature description ability for each pixel. Next, this study formulates segmentation task as a classification problem and solves it with a more contributing 3D modified attention U-Net as a two-label classifier for reducing computational cost. This proposed network contains an upsampling to raise image resolution before encoding and revert image to its original size with a downsampling after three max-pooling layers. Besides, the attention gate (AG) set in these layers contributes to more accurate segmentation by maintaining details while suppressing noises. Finally, the experimental results on three publicly available datasets DRIVE, STARE, and HRF demonstrate better performance than most existing methods.

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