اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدParallelization of the multi-level hp-adaptive finite cell method
57
0
0.0
(
0
)
تأليف
John N. Jomo
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes, a hp-scheme based on spatial refinement by superposition. An efficient parallelization of this method using standard domain decomposition approaches in combination with ghost elements faces the challenge of a large basis function support resulting from the overlay structure and is in many cases not feasible. In this contribution, a parallelization strategy for the multi-level hp-scheme is presented that is adapted to the schemes simple hierarchical structure. By distributing the computational domain among processes on the granularity of the active leaf elements and utilizing shared mesh data structures, good parallel performance is achieved, as redundant computations on ghost elements are avoided. We show the schemes parallel scalability for problems with a few hundred elements per process. Furthermore, the scheme is used in conjunction with the finite cell method to perform numerical simulations on domains of complex shape.
قيم البحث
اقرأ أيضاً
The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based on removal
of basis functions associated with badly cut cells by introducing carefully designed constraints, which results in well-posed systems of linear algebraic equations, while preserving the optimal approximation order of the underlying finite element spaces. The specific goal of this work is to present the implementation and performance of the method on distributed-memory platforms aiming at the efficient solution of large-scale problems. In particular, we show that, by considering AgFEM, the resulting systems of linear algebraic equations can be effectively solved using standard algebraic multigrid preconditioners. This is in contrast with previous works that consider highly customized preconditioners in order to allow one the usage of iterative solvers in combination with unfitted techniques. Another novelty with respect to the methods available in the literature is the problem sizes that can be handled with the proposed approach. While most of previous references discussing linear solvers for unfitted methods are based on serial non-scalable algorithms, we propose a parallel distributed-memory method able to efficiently solve problems at large scales. This is demonstrated by means of a weak scaling test defined on complex 3D domains up to 300M degrees of freedom and one billion cells on 16K CPU cores in the Marenostrum-IV platform. The parallel implementation of the AgFEM method is available in the large-scale finite element package FEMPAR.
Graphics Processing Unit (GPU) computing is becoming an alternate computing platform for numerical simulations. However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of problems. To this
end, numerical accuracies and computational work of several numerical methods are compared using a GPU computing implementation. The Correction Procedure via Reconstruction (CPR), Discontinuous Galerkin (DG), Nodal Discontinuous Galerkin (NDG), Spectral Difference (SD), and Finite Volume (FV) methods are investigated using various reconstruction orders. Both smooth and discontinuous cases are considered for two-dimensional simulations. For discontinuous problems, MUSCL schemes are employed with FV, while CPR, DG, NDG, and SD use slope limiting. The computation time to reach a set error criteria and total time to complete solutions are compared across the methods. It is shown that while FV methods can produce solutions with low computational times, they produce larger errors than high-order methods for smooth problems at the same order of accuracy. For discontinuous problems, the methods show good agreement with one another in terms of solution profiles, and the total computational times between FV, CPR, and SD are comparable.
A mixed finite element method combining an iso-parametric $Q_2$-$P_1$ element and an iso-parametric $P_2^+$-$P_1$ element is developed for the computation of multiple cavities in incompressible nonlinear elasticity. The method is analytically proved
to be locking-free and convergent, and it is also shown to be numerically accurate and efficient by numerical experiments. Furthermore, the newly developed accurate method enables us to find an interesting new bifurcation phenomenon in multi-cavity growth.
We present our experience with the modernization on the GR-MHD code BHAC, aimed at improving its novel hybrid (MPI+OpenMP) parallelization scheme. In doing so, we showcase the use of performance profiling tools usable on x86 (Intel-based) architectur
es. Our performance characterization and threading analysis provided guidance in improving the concurrency and thus the efficiency of the OpenMP parallel regions. We assess scaling and communication patterns in order to identify and alleviate MPI bottlenecks, with both runtime switches and precise code interventions. The performance of optimized version of BHAC improved by $sim28%$, making it viable for scaling on several hundreds of supercomputer nodes. We finally test whether porting such optimizations to different hardware is likewise beneficial on the new architecture by running on ARM A64FX vector nodes.
We present a new technique for transferring momentum and velocity between particles and grid with Particle-In-Cell (PIC) calculations which we call Affine-Particle-In-Cell (APIC). APIC represents particle velocities as locally affine, rather than loc
ally constant as in traditional PIC. We show that this representation allows APIC to conserve linear and angular momentum across transfers while also dramatically reducing numerical diffusion usually associated with PIC. Notably, conservation is achieved with lumped mass, as opposed to the more commonly used Fluid Implicit Particle (FLIP) transfers which require a full mass matrix for exact conservation. Furthermore, unlike FLIP, APIC retains a filtering property of the original PIC and thus does not accumulate velocity modes on particles as FLIP does. In particular, we demonstrate that APIC does not experience velocity instabilities that are characteristic of FLIP in a number of Material Point Method (MPM) hyperelasticity calculations. Lastly, we demonstrate that when combined with the midpoint rule for implicit update of grid momentum that linear and angular momentum are exactly conserved.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
