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Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
We extend the scope of analysis for linesearch optimization algorithms on (possibly infinite-dimensional) Riemannian manifolds to the convergence analysis of the BFGS quasi-Newton scheme and the
Effect of non-linear permeability in a spherically symmetric model of hydrocephalus.
TLDR
A spherically symmetric model of the brain is examined and non-linear effects tend to improve predictions of ventricle wall displacement and pressure increase in acute hydrocephalus in comparison with a constant permeability model.
An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus.
TLDR
The equations for axisymmetric and fully 3D models of a hydrocephalic brain are formulated and the effect of hydrostatic pressure variation is considered.
Time‐Discrete Geodesics in the Space of Shells
TLDR
A computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell, is offered, which emphasizes the strong impact of physical parameters on the evolution of a shell shape along a geodesic path.
A Nonlinear Elastic Shape Averaging Approach
TLDR
A physically motivated approach is presented for computing a shape average of a given number of shapes, which minimizes the total elastic energy stored in these deformations and is invariant under rigid body motions.
A Continuum Mechanical Approach to Geodesics in Shape Space
TLDR
The proposed shape metric is derived from a continuum mechanical notion of viscous dissipation and implemented via a level set representation of shapes, and a finite element approximation is employed as spatial discretization both for the pairwise matching deformations and for the level set representations.
Variational time discretization of geodesic calculus
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete
Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds
TLDR
This work generalizes the notion of Bezier surfaces and surface splines to Riemannian manifolds and proposes an algorithm to optimize the BeZier control points given a set of points to be interpolated by a Beziers surface spline.
Analytic solution during an infusion test of the linear unsteady poroelastic equations in a spherically symmetric model of the brain.
TLDR
This work determines the spatial and temporal distribution of cerebrospinal fluid (CSF) pressure and brain displacement during an infusion test in a spherically symmetric, three-component poroelastic model of the brain.
A simple and efficient scheme for phase field crystal simulation
We propose an unconditionally stable semi-implicit time discretization of the phase field crystal evolution. It is based on splitting the underlying energy into convex and concave parts and then
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