Publication

A semi-continuous formulation for goal-oriented reduced-order models: 1D problems

Stefano Mattei
2016
Journal Articles

Abstract

A semi-continuous formulation is introduced for finding bases that minimise the error in a specific output functional of a reduced-order model. The formulation is advantageous in that it can be used with arbitrary reference data and can be easily applied to nonlinear models and functionals. A general description of the approach is given; then, explicit formulations are derived for the advection-diffusion and Burgers' equations. Numerical results are given for both linear and nonlinear functionals. These show substantial reductions in error when compared with POD modes, depending on the functional considered. The optimisation of bases for a reduced-order model using an approximated governing equation is also described, for which large increases in accuracy are obtained relative to POD modes. Copyright (C) 2015 John Wiley & Sons, Ltd.

Official source

https://infoscience.epfl.ch/entities/publication/309b9105-243a-47c5-9c29-050dc5c5a403

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Stefano Mattei
2016
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/309b9105-243a-47c5-9c29-050dc5c5a403

About this result

Related concepts (9)

Functional programming

In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can.

Data type

In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data.

Recursive data type

In computer programming languages, a recursive data type (also known as a recursively-defined, inductively-defined or inductive data type) is a data type for values that may contain other values of the same type. Data of recursive types are usually viewed as directed graphs. An important application of recursion in computer science is in defining dynamic data structures such as Lists and Trees. Recursive data structures can dynamically grow to an arbitrarily large size in response to runtime requirements; in contrast, a static array's size requirements must be set at compile time.

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A semi-continuous formulation for goal-oriented reduced-order models: 1D problems

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