A GPU‐Adapted Structure for Unstructured Grids
A key advantage of working with structured grids (e.g., images) is the ability to directly tap into the powerful machinery of linear algebra. This is not much so for unstructured grids where intermediate bookkeeping data structures stand in the way. On modern high performance computing hardware, the...
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| Vydané v: | Computer graphics forum Ročník 36; číslo 2; s. 495 - 507 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Oxford
Blackwell Publishing Ltd
01.05.2017
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | A key advantage of working with structured grids (e.g., images) is the ability to directly tap into the powerful machinery of linear algebra. This is not much so for unstructured grids where intermediate bookkeeping data structures stand in the way. On modern high performance computing hardware, the conventional wisdom behind these intermediate structures is further challenged by costly memory access, and more importantly by prohibitive memory resources on environments such as graphics hardware. In this paper, we bypass this problem by introducing a sparse matrix representation for unstructured grids which not only reduces the memory storage requirements but also cuts down on the bulk of data movement from global storage to the compute units. In order to take full advantage of the proposed representation, we augment ordinary matrix multiplication by means of action maps, local maps which encode the desired interaction between grid vertices. In this way, geometric computations and topological modifications translate into concise linear algebra operations. In our algorithmic formulation, we capitalize on the nature of sparse matrix‐vector multiplication which allows avoiding explicit transpose computation and storage. Furthermore, we develop an efficient vectorization to the demanding assembly process of standard graph and finite element matrices. |
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| AbstractList | A key advantage of working with structured grids (e.g., images) is the ability to directly tap into the powerful machinery of linear algebra. This is not much so for unstructured grids where intermediate bookkeeping data structures stand in the way. On modern high performance computing hardware, the conventional wisdom behind these intermediate structures is further challenged by costly memory access, and more importantly by prohibitive memory resources on environments such as graphics hardware. In this paper, we bypass this problem by introducing a sparse matrix representation for unstructured grids which not only reduces the memory storage requirements but also cuts down on the bulk of data movement from global storage to the compute units. In order to take full advantage of the proposed representation, we augment ordinary matrix multiplication by means of action maps, local maps which encode the desired interaction between grid vertices. In this way, geometric computations and topological modifications translate into concise linear algebra operations. In our algorithmic formulation, we capitalize on the nature of sparse matrix-vector multiplication which allows avoiding explicit transpose computation and storage. Furthermore, we develop an efficient vectorization to the demanding assembly process of standard graph and finite element matrices. |
| Author | Steinberger, Markus Zayer, Rhaleb Seidel, Hans‐Peter |
| Author_xml | – sequence: 1 givenname: Rhaleb surname: Zayer fullname: Zayer, Rhaleb organization: Saarland Informatics Campus – sequence: 2 givenname: Markus surname: Steinberger fullname: Steinberger, Markus organization: Saarland Informatics Campus – sequence: 3 givenname: Hans‐Peter surname: Seidel fullname: Seidel, Hans‐Peter organization: Saarland Informatics Campus |
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| Copyright | 2017 The Author(s) Computer Graphics Forum © 2017 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2017 The Eurographics Association and John Wiley & Sons Ltd. |
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| Title | A GPU‐Adapted Structure for Unstructured Grids |
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