scholarly journals Well-solvable cases of the QAP with block-structured matrices

2015 ◽  
Vol 186 ◽  
pp. 56-65 ◽  
Author(s):  
Eranda Çela ◽  
Vladimir G. Deineko ◽  
Gerhard J. Woeginger
Keyword(s):  
Structured Matrices ◽  
Block Structured

scholarly journals A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices

2016 ◽  
Vol 2016 ◽  
pp. 1-3 ◽  
Author(s):  
Hal Caswell ◽  
Silke F. van Daalen
Keyword(s):  
Simple Formula ◽  
Column Vector ◽  
Structured Matrices ◽  
Structured Matrix ◽  
Block Structured

The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes.

scholarly journals Block Representation and Spectral Properties of Constant Sum Matrices

2018 ◽  
Vol 34 ◽  
pp. 170-190 ◽  
Author(s):  
Sally Hill ◽  
Matthew Lettington ◽  
Karl Michael Schmidt
Keyword(s):  
Spectral Properties ◽  
Structured Matrices ◽  
Eigenvalues And Eigenvectors ◽  
Equivalent Representation ◽  
Symmetry Properties ◽  
Explicit Formulae ◽  
Block Structured

An equivalent representation of constant sum matrices in terms of block-structured matrices is given in this paper. This provides an easy way of constructing all constant sum matrices, including those with further symmetry properties. The block representation gives a convenient description of the dihedral equivalence of such matrices. It is also shown how it can be used to study their spectral properties, giving explicit formulae for eigenvalues and eigenvectors in special situations, as well as for quasi-inverses when these exist.

Algorithmic Logic with Recursive Functions

1981 ◽  
Vol 4 (4) ◽  
pp. 975-995
Author(s):  
Andrzej Szałas
Keyword(s):  
Completeness Theorem ◽  
Inference Rules ◽  
Partial Correctness ◽  
Recursive Functions ◽  
Algorithmic Logic ◽  
Block Structured

A language is considered in which the reader can express such properties of block-structured programs with recursive functions as correctness and partial correctness. The semantics of this language is fully described by a set of schemes of axioms and inference rules. The completeness theorem and the soundness theorem for this axiomatization are proved.

scholarly journals AMReX: Block-structured adaptive mesh refinement for multiphysics applications

2021 ◽  
pp. 109434202110228
Author(s):  
Weiqun Zhang ◽  
Andrew Myers ◽  
Kevin Gott ◽  
Ann Almgren ◽  
John Bell
Keyword(s):  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Uniform Mesh ◽  
Physical Processes ◽  
Structured Adaptive Mesh Refinement ◽  
Core Elements ◽  
Accelerator Design ◽  
Block Structured

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

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