Zobrazeno 1 - 10
of 136
pro vyhledávání: '"Tsuchiya, Takuya"'
Autor:
Suzuki, Takashi, Tsuchiya, Takuya
We study Hadamard's variational formula for simple eigenvalues under dynamical and conformal deformations. Particularly, harmonic convexity of the first eigenvalue of the Laplacian under the mixed boundary condition is established for two-dimensional
Externí odkaz:
http://arxiv.org/abs/2409.04021
In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lema\^itre--Robertson--Walker spacetime. To evaluate the numerical stability, we calculate the con
Externí odkaz:
http://arxiv.org/abs/2407.14305
Autor:
Kobayashi, Kenta, Tsuchiya, Takuya
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error
Externí odkaz:
http://arxiv.org/abs/2402.18860
Autor:
Suzuki, Takashi, Tsuchiya, Takuya
We study Hadamard variation of eigenvalues of Laplacian with respect to general domain perturbations. We show their existence up to the second order rigorously and characterize the derivatives, using associated eigenvalue problems in finite dimension
Externí odkaz:
http://arxiv.org/abs/2309.00273
Autor:
Tsuchiya, Takuya, Nakamura, Makoto
Publikováno v:
JSIAM Letters vol. 15, pp. 45--48 (2023)
Numerical simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime are performed. We use two structure-preserving discrete forms of the Klein--Gordon equation. The disparity between the two forms is the discretization of the di
Externí odkaz:
http://arxiv.org/abs/2211.09031
Autor:
Suzuki, Takashi, Tsuchiya, Takuya
Publikováno v:
Journal of Mathematical Society of Japan, 75 (2023) 983--1024
We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then, relations to
Externí odkaz:
http://arxiv.org/abs/2210.00693
In this study, we investigate the numerical stability of the covariant BSSN (cBSSN) formulation proposed by Brown. We calculate the constraint amplification factor (CAF), which is an eigenvalue of the coefficient matrix of the evolution equations of
Externí odkaz:
http://arxiv.org/abs/2206.13944
Autor:
Tsuchiya, Takuya, Nakamura, Makoto
We perform some simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime. We reported the accurate numerical results of the equation with the structure-preserving scheme (SPS) in an earlier publication (Tsuchiya and Nakamura in
Externí odkaz:
http://arxiv.org/abs/2203.09074
Publikováno v:
JSIAM Letters Vol. 14 (2022) pp. 84-87
We perform simulations in a gravitational collapsing model using the Einstein equations. In this paper, we review the equations for constructing the initial values and the evolution form of the Einstein equations called the BSSN formulation. In addit
Externí odkaz:
http://arxiv.org/abs/2203.05149
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the diameter of a s
Externí odkaz:
http://arxiv.org/abs/2106.03339