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Saito Lab
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The lab gives mathematical foundations to the numerical computation of differential equations.
AboutAbout the lab
Making numerical computation reliable through mathematics.
The Saito Lab studies the numerical analysis of partial differential equations.
The lab systematically derives methods for converting differential equations, as mathematical models, into forms that can be computed by finite difference methods, finite element methods, and others, and verifies their mathematical correctness.
It uses mathematics to systematize the "artisanal know-how" that has relied on experience, aiming for high-quality simulation methods that even people with little experience can use with confidence.
Toward pure mathematics, the lab also aims to present new problem formulations suited to computation and to open up new research areas in the theory of differential equations.
Key terms
- Mathematical model
- A description of how a phenomenon works, expressed in mathematical form such as equations
- Finite element method
- A computational method that divides the region of interest into small pieces such as triangles and finds an approximate solution of an equation on each piece
- Discretization
- The process of representing a continuously varying quantity by its values at separate points, converting it into a form that a computer can handle
ResearchResearch themes
From the standpoint of numerical analysis, the lab builds the mathematical foundations of numerical computation techniques for a wide variety of mathematical models. It works on deriving the computational models obtained by discretizing differential equations and on establishing their mathematical validity.
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MembersFaculty
- ProfessorNorikazu SaitoPublications ↗
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Example finite element mesh, for illustrating the concept” SamitchSandia / CC BY-SA 4.0 (cropped)
- Discretization Methods such as the Finite Element Method: “Finite element mesh” Bruno Sudret / CC BY 4.0 (cropped)
- Related lab (Kashiwabara Lab): “Karmansche Wirbelstr kleine Re” Jürgen Wagner / CC BY-SA 4.0 (cropped)
- Related lab (Hasegawa Lab): “Lambda cube” Денис Москвин / Public domain (cropped)
- Related lab (Shimomura Lab): “Traveling wave” P.wormer / CC BY-SA 3.0 (cropped)
- Related lab (Matui Lab): “Cantors cube” User:Solkoll / Public domain (cropped)
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