Kyushu University [Yoshitaka Watanabe (Associate Professor) Research Institute for Information Technology, Section of Advanced Computational Science]

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Researcher information

Yoshitaka Watanabe
Associate Professor
Section of Advanced Computational Science
Research Institute for Information Technology
Last modified date：2024.04.17

Graduate School

Department of informatics
Graduate School of Information Science and Electrical Engineering

Undergraduate School

Department of Electrical Engineering and Computer Science
School of Engineering

Department of Physics
School of Sciences

School of Engineering

Other Organization

Data-Driven Innovation Initiative

E-Mail

Homepage

Academic Degree

Country of degree conferring institution (Overseas)

Field of Specialization

Total Priod of education and research career in the foreign country

Research

Research Interests

a posteriori estimate for solutions of nonlinear PDE
keyword : PDF, Numerical verification, FEM
2002.04.

Academic Activities

Books

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Mitsuhiro T. Nakao, Michael Plum, and Yoshitaka Watanabe, Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations, Springer Singapore, ISBN 978-981-13-7669-6, 2019.11, 精度保証付き数値計算および計算機援用証明の詳細について、特に非線形偏微分方程式の解に対する存在と厳密な誤差上界をコンピュータによって把握する理論と計算アルゴリズムおよびプログラミングを解説した書籍。.

Papers

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1.	Yoshitaka Watanabe, Tomoyuki Miyaji, Another computer-assisted proof of unimodality of solutions for Proudman Johnson equation, Japan Journal of Industrial and Applied Mathematics, (published online) 03 January, 2024, https://doi.org/10.1007/s13160-023-00639-x, 2024.01.
2.	Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, On some convergence properties for finite element approximations to the inverse of linear elliptic operators, Acta Cybernetica, https://doi.org/10.14232/actacyb.294906, 26, 1, 71-82, 2023.06.
3.	Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, Efficient approaches for verifying the existence and bound of inverse of linear operators in Hilbert spaces, Journal of Scientific Computing, https://doi.org/10.1007/s10915-023-02097-6, 94, Article number: 43, 2023.01, 2階楕円型作用素において得られたこれまでの成果を拡張・一般化することで、一般のヒルベルト空間における無限次元線形作用素の可逆性の検証と、逆作用素ノルムの数学的に厳密な意味での上界を求める新しい精度保証付き数値計算アルゴリズムを提案し、多次元微分作用素を含む応用問題から導かれる具体的な検証例を与えることに成功した。.
4.	Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao, Inclusion method of optimal constant with quadratic convergence for H10-projection error estimates and its applications, Journal of Computational and Applied Mathematics, https://doi.org/10.1016/j.cam.2022.114521, 417, 114521, 2023.01.
5.	Kenta Kobayashi, Yoshitaka Watanabe, Improvement of infinity norm estimations related to computer-assisted proofs of the Kolmogorov problem, JSIAM Letters, https://doi.org/10.14495/jsiaml.14.92 , 14, 92-95, 2022.07.
6.	Shuting Cai, Yoshitaka Watanabe, Computer-assisted proofs of the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem, Journal of Computational and Applied Mathematics, https://doi.org/10.1016/j.cam.2021.113603, 395, 113603, 2021.11, 2次元Navier-Stokes方程式に特別な外力項を課したKolmogorov問題に対し、その2次分岐点にあたる対称性破壊分岐点が真に存在することを、計算機援用証明によって具体的な誤差評価付きで明らかにした。.
7.	Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, Some improvements of invertibility verifications for second-order linear elliptic operators, Applied Numerical Mathematics, 10.1016/j.apnum.2020.03.016, 154, 36-46, 2020.08, This paper presents some computer-assisted procedures to prove the invertibility of a second-order linear elliptic operator and to compute a bound for the norm of its inverse. These approaches are based on constructive L²-norm estimates of the Laplacian and improve on previous procedures that use projection and a priori error estimations. Several examples which confirm the actual effectiveness of the procedures are reported..
8.	Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces, Journal of Differential Equations , 10.1016/j.jde.2018.10.027, 266, 9, 5431-5447, 2019.04, In the present paper, we propose a computer-assisted procedure to prove the invertibility of a linear operator in a Hilbert space and to compute a verified norm bound of its inverse. A number of the authors have previously proposed two verification approaches that are based on projection and constructive a priori error estimates. The approach of the present paper is expected to bridge the gap between the two previous procedures in actual numerical verifications. Several verification examples that confirm the actual effectiveness of the proposed procedure are reported..
9.	Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao, Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-016-0223-y, 33, 3, 629-636, 2016.12.
10.	Yoshitaka Watanabe, An Efficient Numerical Verification Method for the Kolmogorov Problem of Incompressible Viscous Fluid, Journal of Computational and Applied Mathematics, 10.1016/j.cam.2016.01.055, 302, 157-170, 2016.09.
11.	Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao, Norm Bound Computation for Inverses of Linear Operators in Hilbert Spaces, Journal of Differential Equations , 10.1016/j.jde.2015.12.041, 260, 7, 6363-6374, 2016.04, 無限次元Hilbert空間における線形作用素に対し、可逆性の保証と逆作用素ノルムの具体的な上界値を数学的に厳密な意味で計算機で与える一般理論を構築するとともに、与えた上界が最適な作用素ノルムに収束することを明らかにしました。さらに、具体的な問題に対する計算機援用証明により、その有効性を明らかにしました.
12.	Yoshitaka Watanabe, Mitsuhiro T. Nakao, A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration, Applied Mathematics and Computation, doi:10.1016/j.amc.2015.12.021, 276, 239-251, 2016.03, 無限次元Hilbert空間の非線形関数方程式に対し、弱形式に基づく残差引き戻しと無限次元Newton法を組み合わせた堅牢な解の存在検証理論を提案し、非線形偏微分方程式を含む具体的な問題に対する計算機援用証明により、その有効性を明らかにしました。.
13.	Shuting Cai, Yoshitaka Watanabe, A Computer-assisted Method for Excluding Eigenvalues of an Elliptic Operator Linearized at a Solution of a Nonlinear Problem, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-015-0167-7, 32, 1, 263-294, 2015.03.
14.	Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takehiko Kinoshita, Takuma Kimura, Nobito Yamamoto, Some Considerations of the Invertibility Verifications for Linear Elliptic Operators, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-014-0160-6 , 32, 1, 19-32, 2015.03.
15.	Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao, Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces, SIAM Journal on Numerical Analysis, 10.1137/120894683, 52, 2, 975-992, 2014.05, 無限次元Hilbert空間における複素数固有値問題の固有値の数学的に厳密な非存在範囲を与える一般定理と、具体的な非存在領域を求めるための精度保証付き数値計算アルゴリズムを提案するとともに、丸め誤差の影響を考慮した具体的な数値例を確認可能なプログラムコードとともに与えた。.
16.	Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, A Posteriori Estimates of Inverse Operators for Boundary Value Problems in Linear Elliptic Partial Differential Equations, Mathematics of Computation, 82, 283, 1543-1557, 2013.07.
17.	Nobito Yamamoto, Mitsuhiro T. Nakao, Yoshitaka Watanabe, A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations, Numerical Functional Analysis and Optimization, 32, 11, 1190-1204, 2011.11, Nobito Yamamoto, Mitsuhiro T. Nakao, and Yoshitaka Watanabe:.
18.	Mitsuhiro T. Nakao, and Yoshitaka Watanabe, Numerical Verification Methods for Solutions of Semilinear Elliptic Boundary Value Problems, Nonlinear Theory and Its Applications, 2, 1, 2-31, 2011.01.
19.	Yoshitaka Watanabe and Mitsuhiro T. Nakao, Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh-Bénard Problem, Japan Journal of Industrial and Applied Mathematics, 26, 2-3, 443-463, 2009.10.
20.	Yoshitaka Watanabe, Michael Plum, Mitsuhiro T. Nakao , A computer-assisted instability proof for the Orr-Sommerfeld problemwith Poiseuille flow, Journal of Applied Mathematics and Mechanics (ZAMM), Vol.89, No.1, 5-18, 2009.01.
21.	Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe and Takaaki Nishida, A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Be\'nard problems, Numerische Mathematik, Vol.111, No.3, pp.389-406, 2009.01.

Presentations

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1.	Yoshitaka Watanabe, Some computer-assisted proofs for nonlinear differential equations involved with self-similar blowup in wave equations, Nonlinear Analysis, Spectral theory and PDEs, Workshop in Honor of Prof. Dr. Michael Plum, 2024.02.
2.	Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Birgit Schörkhuber, Mitsuhiro T. Nakao, A computer-assisted proof for a nonlinear differential equation involved with self-similar blowup in wave equations, Minisymposia: Verified Numerical Computations and Applications, in the 10th International Congress on Industrial and Applied Mathematics (ICIAM), 2023.08.
3.	Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Takehiko Kinoshita, Mitsuhiro T. Nakao, A computer-assisted proof toward the critical Reynolds number for the Orr-Sommerfeld problem, nternational Workshop on Reliable Computing and Computer-Assisted Proofs (ReCAP 2022), 2022.03.
4.	akehiko Kinoshita, Yoshitaka Watanabe, and Mitsuhiro T. Nakao, On some convergence properties for finite element approximations to the inverse of linear elliptic operators, 19th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2020), 2021.09.
5.	Yoshitaka Watanabe, Computer-assisted proofs for the Orr-Sommerfeld equation, Rigorous Computational Dynamics in Infinite Dimensions, 2019.04.
6.	Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto and Mitsuhiro T. Nakao, A higher order error estimation for finite element approximations of the Poisson equation, 18th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2018), 2018.09.
7.	Yoshitaka Watanabe, Michael Plum, Kaori Nagatou and Mitsuhiro T. Nakao, Verified computations of eigenvalue exclosures for linearized Kolmogorov problem, 18th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2018), 2018.09.
8.	Yoshitaka Watanabe, A higher order error estimation of the Poisson equation and its applications , International Workshop on Numerical Methods for Partial Differential Equations , 2018.03.
9.	Yoshitaka Watanabe, Some computer-assisted proofs for the Navier-Stokes equations, Rigorous Numerics for Infinite Dimensional Nonlinear Dynamics (17w5141), 2017.05.
10.	Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, An alternative approach of invertibility verifications for linear operators in Hilbert spaces, The International Workshop on Numerical Verification and its Applications 2017 (INVA 2017), 2017.03.
11.	Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, Validated constructive error estimatations for bi-harmonic problems, 17th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2016), 2016.09.
12.	Yoshitaka Watanabe, A nonlinear PDE verification -- Fukuoka, Karlsruhe, Nonlinear PDE Days, 2015.07.
13.	Yoshitaka Watanabe, Computer-assisted stability and instability proofs for the Orr-Sommerfeld problem, Institutskolloquien, Institut für Analysis, Karlsruher Institut für Technologie, 2014.09.
14.	Yoshitaka Watanabe, A comparison of computer-assisted proofs for the Kolmogorov problem, International Workshop on Numerical Verification and its Applications 2014 (INVA2014), 2014.03.

Awards

It is selected in the journal JJIAM.

Educational

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