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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer

The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer

Leygue, Adrien
Keunings, Roland
Chinesta, Francisco

Paperback

Series: Springerbriefs in Applied Sciences and Technology

Technology & EngineeringGeneral Computers

ISBN10: 3319028642
ISBN13: 9783319028644
Publisher: Springer Nature
Published: Oct 18 2013
Pages: 117
Weight: 0.43
Height: 0.28 Width: 6.14 Depth: 9.21
Language: English

Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom.

Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters.

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