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Proper Orthogonal Decomposition Methods for Partial Differential Equations

by Zhendong Luo

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A technical guide to POD reduced-order methods for time-dependent PDEs

$174.42 USD
$174.42 USD $174.42 USD

Paperback New English

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AlbakiReads Editorial

A technical guide to POD reduced-order methods for time-dependent PDEs

Zhendong Luo’s book examines proper orthogonal decomposition (POD) as a reduced-order numerical approach for partial differential equations, framing it around computational efficiency, calculation load, and truncation-error accumulation. It begins with foundations in finite-difference, finite-element, and finite-volume-element methods, then develops time-dependent PDE models through numerical procedures, implementation details, and error analysis. The examples span parabolic, hyperbolic, and nonlinear PDE systems. Graphical numerical outputs and comparisons with traditional methods make the volume especially oriented toward applying and assessing POD techniques in computational mathematics and research settings.

Good fit for readers who enjoy

  • Researchers adapting reduced-order numerical methods to PDE problems
  • Graduate-level learners studying numerical analysis of time-dependent PDEs
  • Applied mathematicians working with finite-difference, finite-element, or finite-volume-element methods

Themes

Proper orthogonal decompositionReduced-order numerical methodsTime-dependent partial differential equationsNumerical implementation and error analysisComputational efficiency

Based on publisher information and book metadata.

Book overview

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems.

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