scholarly journals A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing

2010 ◽  
Vol 13 (4) ◽  
pp. 161-175 ◽  
Author(s):  
Christian Wieners
Keyword(s):  
Data Structure ◽  
Finite Elements ◽  
Multigrid Methods ◽  
Geometric Data

scholarly journals Efficient Data Structures for Range Shortest Unique Substring Queries

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 276
Author(s):  
Paniz Abedin ◽  
Arnab Ganguly ◽  
Solon P. Pissis ◽  
Sharma V. Thankachan
Keyword(s):  
Information Retrieval ◽  
Data Structure ◽  
Data Structures ◽  
Query Time ◽  
Geometric Data ◽  
Small Constant ◽  
Efficient Data ◽  
Online Queries ◽  
Efficient Data Structures ◽  
Unique Substrings

Let T[1,n] be a string of length n and T[i,j] be the substring of T starting at position i and ending at position j. A substring T[i,j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T. Repeats and unique substrings are of great interest in computational biology and information retrieval. Given string T as input, the Shortest Unique Substring problem is to find a shortest substring of T that does not occur elsewhere in T. In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over T answering the following type of online queries efficiently. Given a range [α,β], return a shortest substring T[i,j] of T with exactly one occurrence in [α,β]. We present an O(nlogn)-word data structure with O(logwn) query time, where w=Ω(logn) is the word size. Our construction is based on a non-trivial reduction allowing for us to apply a recently introduced optimal geometric data structure [Chan et al., ICALP 2018]. Additionally, we present an O(n)-word data structure with O(nlogϵn) query time, where ϵ>0 is an arbitrarily small constant. The latter data structure relies heavily on another geometric data structure [Nekrich and Navarro, SWAT 2012].

Efficient Handling of Implicit Entities in Reduced Mesh Representations

2005 ◽  
Vol 5 (4) ◽  
pp. 348-359 ◽  
Author(s):  
Waldemar Celes ◽  
Glaucio H. Paulino ◽  
Rodrigo Espinha
Keyword(s):  
Data Structure ◽  
Finite Elements ◽  
State Of The Art ◽  
Point Of View ◽  
Effective Strategy ◽  
Topological Information ◽  
Memory Space ◽  
Reduced Representation ◽  
Application Point ◽  
Reduced Representations

State-of-the-art numerical analyses require mesh representation with a data structure that provides topological information. Due to the increasing size of the meshes currently used for simulating complex behaviors with finite elements or boundary elements (e.g., adaptive and/or coupled analyses), several researchers have proposed the use of reduced mesh representations. In a reduced representation, only a few types of the defined topological entities are explicitly represented; all the others are implicit and retrieved “on-the-fly,” as required. Despite being very effective in reducing the memory space needed to represent large models, reduced representations face the challenge of ensuring the consistency of all implicit entities when the mesh undergoes modifications. As implicit entities are usually described by references to explicit ones, modifying the mesh may change the way implicit entities (which are not directly modified) are represented, e.g., the referenced explicit entities may no longer exist. We propose a new and effective strategy to treat implicit entities in reduced representations, which is capable of handling transient nonmanifold configurations. Our strategy allows, from the application point of view, explicit and implicit entities to be interchangeably handled in a uniform and transparent way. As a result, the application can list, access, attach properties to, and hold references to implicit entities, and the underlying data structure ensures that all such information remains valid even if the mesh is modified. The validity of the proposed approach is demonstrated by running a set of computational experiments on different models subjected to dynamic remeshing operations.

Deformation simulation using cubic finite elements and efficient p-multigrid methods

2015 ◽  
Vol 53 ◽  
pp. 185-195 ◽  
Author(s):  
Daniel Weber ◽  
Johannes Mueller-Roemer ◽  
Christian Altenhofen ◽  
André Stork ◽  
Dieter Fellner
Keyword(s):  
Finite Elements ◽  
Multigrid Methods ◽  
Deformation Simulation
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