9 citations · 34 across the 19 of their papers we have counts for
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A preconditioning technique of Gauss--Legendre quadrature for the logarithm of symmetric positive definite matrices
Fuminori Tatsuoka, Tomohiro Sogabe, Tomoya Kemmochi +1
This note considers the computation of the logarithm of symmetric positive definite matrices using the Gauss--Legendre (GL) quadrature. The GL quadrature becomes slow when the cond…
Higher order discrete gradient method by the discontinuous Galerkin time-stepping method
Tomoya Kemmochi
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems…
Computing the matrix exponential with the double exponential formula
Fuminori Tatsuoka, Tomohiro Sogabe, Tomoya Kemmochi +1
This paper considers the computation of the matrix exponential with numerical quadrature. Although several quadrature-based algorithms have been proposed, they focus…
Matrix equation representation of the convolution equation and its unique solvability
Yuki Satake, Tomohiro Sogabe, Tomoya Kemmochi +1
We consider the convolution equation , where and are given, and is to be determined. T…
Discrete maximal regularity for the discontinuous Galerkin time-stepping method without logarithmic factor
Takahito Kashiwabara, Tomoya Kemmochi
Maximal regularity is a kind of a priori estimates for parabolic-type equations and it plays an important role in the theory of nonlinear differential equations. The aim of this pa…
Discrete maximal regularity for the finite element approximation of the Stokes operator and its application
Tomoya Kemmochi
Maximal regularity for the Stokes operator plays a crucial role in the theory of the non-stationary Navier--Stokes equations. In this paper, we consider the finite element semi-dis…
A structure-preserving numerical method for the fourth-order geometric evolution equations for planar curves
E. Miyazaki, T. Kemmochi, T. Sogabe +1
For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy, including the Willmore and the Helfrich flows, we consider a numerical…
-resolvent estimate for finite element approximation of the Stokes operator
Tomoya Kemmochi
In this paper, we will show the -resolvent estimate for the finite element approximation of the Stokes operator for , wher…
Structure-preserving numerical methods for constrained gradient flows of planar closed curves with explicit tangential velocities
Tomoya Kemmochi, Yuto Miyatake, Koya Sakakibara
In this paper, we consider numerical approximation of constrained gradient flows of planar closed curves, including the Willmore and the Helfrich flows. These equations have energy…
Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy
Tomoya Kemmochi, Shun Sato
In this paper, we present a novel investigation of the so-called SAV approach, which is a framework to construct linearly implicit geometric numerical integrators for partial diffe…
Computing the matrix fractional power with the double exponential formula
Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake +2
Two quadrature-based algorithms for computing the matrix fractional power are presented in this paper. These algorithms are based on the double exponential (DE) formula, whic…
Modified Strang splitting for semilinear parabolic problems
Kosuke Nakano, Tomoya Kemmochi, Yuto Miyatake +2
We consider applying the Strang splitting to semilinear parabolic problems. The key ingredients of the Strang splitting are the decomposition of the equation into several parts and…
Relation between the T-congruence Sylvester equation and the generalized Sylvester equation
Yuki Satake, Masaya Oozawa, Tomohiro Sogabe +3
The T-congruence Sylvester equation is the matrix equation , where , , and $C\in\mathbb{R}^{m\times m}…
Maximum norm error estimates for the finite element approximation of parabolic problems on smooth domains
Takahito Kashiwabara, Tomoya Kemmochi
In this paper, we consider the finite element approximation for a parabolic problem on a smooth domain with the inhomogeneous Neumann boundary condition. We…
- and -error estimates of linear finite element method for Neumann boundary value problems in a smooth domain
Takahito Kashiwabara, Tomoya Kemmochi
Pointwise error analysis of the linear finite element approximation for in , on , where is a bounded smooth domain in $\mathbb R^…
On the finite element approximation for non-stationary saddle-point problems
Tomoya Kemmochi
In this paper, we present a numerical analysis of the hydrostatic Stokes equations, which are linearization of the primitive equations describing the geophysical flows of the ocean…
Energy dissipative numerical scheme for gradient flows of planar curves using discrete partial derivatives and B-spline curves
Tomoya Kemmochi
In this paper, we develop an energy dissipative numerical scheme for gradient flows of planar curves, such as the curvature flow and the elastic flow. Our study presents a general…
Numerical analysis of elastica with obstacle and adhesion effects
T. Kemmochi
We consider the numerical computation of a variational problem that arises from materials science. The target functional is a type of elastic energy that is influenced by obstacles…
Discrete maximal regularity and the finite element method for parabolic equations
Tomoya Kemmochi, Norikazu Saito
Maximal regularity is a fundamental concept in the theory of partial differential equations. In this paper, we establish a fully discrete version of maximal regularity for a parabo…