Grammar Based Multi-frontal Solver for Isogeometric Analysis in 1D

نویسندگان

  • Krzysztof Kuznik
  • Maciej Paszynski
  • Victor M. Calo
چکیده

In this paper, we present a multi-frontal direct solver for one-dimensional isogeometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the entire solver algorithm, including generation of frontal matrices, merging, and eliminations as a set of basic undividable tasks called graph grammar productions. Having the solver algorithm expressed as GG productions, we can find the partial order of execution and create a dependency graph, allowing for scheduling of tasks into shared memory parallel machine. We focus on the implementation of the solver with NVIDIA CUDA on the graphic processing unit (GPU). The solver has been tested for linear, quadratic, cubic, and higher-order B-splines, resulting in logarithmic scalability.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Grammar-Based Multi-Frontal Solver for One Dimensional Isogeometric Analysis with Multiple Right-Hand-Sides

This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for onedimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm. The integration and the solver algorithm are partitioned into basic indivisible tasks, namely th...

متن کامل

Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis

This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence ...

متن کامل

Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers

In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solver. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O(p log(N/p)) for one dimensional problems, O(Np) for two dimensional problems, and O(Np) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynom...

متن کامل

Computational complexity and memory usage for multi-frontal direct solvers in structured mesh finite elements

The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multifrontal direct solver algorithm on linear systems resulting from B-spline-based isogeometric finite elements, where the mesh is a structured grid. Specifically we provide the es...

متن کامل

Open Source Java Implementation of the Parallel Multi-thread Alternating Direction Isogeometric L2 Projections Solver for Material Science Simulations

This paper describes multi-thread parallel open source JAVA implementation of alternating directions isogeometric L2 projections solver. The solver enables for fast numerical simulations of time-dependent problems. To apply our solver, the time-dependent problem must be discretized using isogeometric finite element method with B-spline basis functions in the spatial domain. The problem is solve...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Computer Science (AGH)

دوره 14  شماره 

صفحات  -

تاریخ انتشار 2013