Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1807.01417

The Implementation of the Colored Abstract Simplicial Complex and its Application to Mesh Generation

C. T. Lee·J. B. Moody·R. E. Amaro·J. A. McCammon·M. Holst
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce CASC: a new, modern, and header-only C++ library which provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly on the simplices at each dimension. This is accomplished by using the latest C++ language features including variadic template parameters introduced in C++11 and automatic function return type deduction from C++14. Effectively CASC decouples the representation of the topology from the interactions of user data. We present the innovations and design principles of the data structure and related algorithms. This includes a metadata aware decimation algorithm which is general for collapsing simplices of any dimension. We also present an example application of this library to represent an orientable surface mesh.

Explore related subjects

cs.MScs.NAmath.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C. T. Lee, J. B. Moody, R. E. Amaro, J. A. McCammon, M. Holst. 2019-03-27. The Implementation of the Colored Abstract Simplicial Complex and its Application to Mesh Generation. https://doi.org/10.1145/3321515

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Ozaki Scheme II: A GEMM-oriented emulation of floating-point matrix multiplication using an integer modular technique

This paper addresses emulation algorithms for matrix multiplication. General Matrix-Matrix Multiplication (GEMM), a fundamental operation in the Basic Linear Algebra Subprograms (BLAS), is typically optimized for specific hardware architectures. The Ozaki scheme is a well-established GEMM-based emulation method for matrix multiplication, wherein input matrices are decomposed into several low-precision components to ensure that the resulting matrix product is computed exactly through numerical operations. This study proposes a novel GEMM-based emulation method for matrix multiplication that leverages the Chinese Remainder Theorem. The proposed method inherits the computational efficiency of highly optimized GEMM routines and further enables control over the number of matrix multiplications, which can enhance computational accuracy. We present numerical experiments featuring INT8 Tensor Core operations on GPUs and FP64 arithmetic on CPUs as case studies. The results demonstrate that FP64 emulation using the proposed method achieves performance levels of up to 7.4 to 9.8 TFLOPS on the NVIDIA RTX 4090 and 56.6 to 80.2 TFLOPS on the NVIDIA GH200, exceeding the measured performance of native FP64 arithmetic. Furthermore, for FP64 computations on CPUs, the proposed method achieved up to a 2.3x speedup in emulating quadruple-precision arithmetic compared to the conventional Ozaki scheme.

cs.MS↗
arXiv2026

Eigensolvers for polynomial roots and tensor decomposition

Computing eigenvalues and eigenvectors is at the heart of the solution of many non-linear problems. For instance, finding the roots of polynomial systems reduces to computing joint eigenvectors of operators of multiplication. Similarly, tensor decomposition can be performed via the joint diagonalization of submatrices of the Catalecticant of the tensor. We describe and illustrate symbolic-numeric methods for computing the solutions of these algebraic problems from the computation of joint eigenvectors of commuting operators, and for analysing their multiplicity structure, as well as their implementation in the package AlgebraicSolvers.jl.

cs.MS↗
arXiv2026

The Art of Closed-Formula Defaults: Search-Free Code Generation for Tensor Operators

Agentic search and automated optimization of GPU kernels are powerful tools for large language model inference. Their effectiveness, however, depends not on the sophistication of the search itself, but on the clarity of the optimization problem being solved. We provide an application-first approach that drives a hierarchical code generation tool from operator specifi cation down to GPU instructions, and show that a clearly defined computational model makes the optimization problem tractable.

cs.MS↗