Computing integrals over polynomially defined regions and their boundaries in 2 and 3 dimensions

DOI10.1016/j.matcom.2011.06.003zbMath1242.65050OpenAlexW2033235834MaRDI QIDQ417963

Stanly L. Steinberg, Michael J. Wester, Yuzita Yaacob

Publication date: 14 May 2012

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2011.06.003

zbMATH Keywords

algorithmsarea integralnumerical examplescylindrical algebraic decompositioniterated integralsdivergence theoremsurface integralvolume integralvector calculusGreen's theoremsline integral

Mathematics Subject Classification ID

Multidimensional problems (41A63) Integration of real functions of several variables: length, area, volume (26B15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (1)

The truncated K-moment problem for closure of open sets

Uses Software

• Mathematica
• QEPCAD

Cites Work

• Partial cylindrical algebraic decomposition for quantifier elimination
• Testing stability by quantifier elimination
• Application of Gröbner bases and quantifier elimination for insightful engineering design
• Solving systems of strict polynomial inequalities
• Solving Polynomial Strict Inequalities Using Cylindrical Algebraic Decomposition
• Local quantifier elimination
• Approximate Volume and Integration for Basic Semialgebraic Sets
• Cylindrical Algebraic Decomposition I: The Basic Algorithm
• Simple CAD construction and its applications

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