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Mathematical Engineering Lab
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A lab that builds fast and accurate computational methods from mathematical theory.
AboutAbout the lab
Faster, higher-accuracy computational algorithms.
The Zhang-Sogabe Lab studies algorithms for fast computation, based on the theory of numerical analysis and applied mathematics.
Using the methods it develops, the lab solves problems that arise in fields such as computational physics through computation on computers.
Its research has two sides: an “algebraic” side that solves equations quickly and accurately, and an “analytic” side that deals with the theory of differential equations and data assimilation.
The lab pursues its research on the idea that the faster computers become, the more the speed of algorithms matters.
Key terms
- Algorithm
- A procedure or set of rules for having a computer carry out a calculation
- Robust
- Able to keep computing well and give answers that do not break down significantly, even when conditions get somewhat worse
- Tensor
- Numbers arranged along three or more directions, such as length, width, and depth. A generalization of the matrix
- Data assimilation
- A method of estimating the current state and the future by combining a mathematical model used for prediction with actually observed data
NewsLab news
A master's student won the Best Award at the Master's Thesis Interim Review of the Department of Applied Physics
An undergraduate student won the Excellent Presentation Award at the Graduation Thesis Review of the Department of Applied Physics
A master's student won the Excellence Award at the Master's Thesis Interim Review of the Department of Applied Physics
An undergraduate student won the Excellent Presentation Award at the Graduation Thesis Review of the Department of Applied Physics
ResearchResearch themes
Understanding and predicting the behavior of natural and artificial systems with a very large number of degrees of freedom requires large-scale computation on computers. Based on the theory of numerical analysis and applied mathematics, the lab develops computational algorithms under the banner of “faster, more accurate, more robust, and more elegant.”
*Illustrative imageNumerical Linear Algebra
The lab develops computational algorithms for solving linear equations, eigenvalue problems, and singular value problems, which are in high demand in physics and engineering. These problems arise in fluid and structural analysis, condensed matter physics, data analysis, and more.
*Illustrative imageComputational Methods from a Tensor Perspective
To study the stability of the linear equations that arise when partial differential equations are discretized, the lab develops efficient computational methods from the perspective of tensors. Even a digital color image can be viewed as a tensor.
*Illustrative imageMatrix Functions and Matrix Equations
The lab studies methods for computing “functions of matrices,” such as the matrix square root, quickly and accurately. More generally, it also develops numerical methods for solving equations whose unknown is a matrix.
*Illustrative imageMathematics of Data Assimilation
Data assimilation is a theory that combines mathematical models with actual data for estimation and prediction, and weather forecasting is a representative application. In many cases it is not yet understood why it works well, and the lab carries out mathematical research that has almost no precedent in Japan.
MembersFaculty
The members of the Zhang-Sogabe Lab consist of faculty, postdoctoral researchers, secretaries, doctoral, master's, and undergraduate students, and graduate research students.As of 2026
- ProfessorShao-Liang Zhang
- ProfessorTomohiro Sogabe
- Assistant ProfessorKota Takeda
VoicesStudent voices
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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: “The catalyst high performance computing (HPC)” ENERGY.GOV / Public domain (cropped)
- Numerical Linear Algebra: “BalticServers data center” BalticServers.com / CC BY-SA 3.0 (cropped)
- Computational Methods from a Tensor Perspective: “Meshing in Finite Element Analysis” Abhiram vs 24 / CC BY-SA 4.0 (cropped)
- Matrix Functions and Matrix Equations: “Strassen-scheme” Fractalone / CC BY-SA 4.0 (cropped)
- Mathematics of Data Assimilation: “Assimilating EarthCARE into numerical weather prediction ESA523298” European Space Agency / CC BY-SA 3.0 igo (cropped)
- Related lab (レオロジー物理工学研究グループ): “Hand in a non-newtonian fluid 05” ElisaG87 / CC BY 4.0 (cropped)
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- Related lab (量子スピン物性工学研究グループ): “Ferrofluid close” Opoterser / CC BY 3.0 (cropped)
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