Periodic solutions of certain large-scale systems of ODEs can be computed ee-ciently using a hybrid Newton{Picard scheme, especially in a continuation context. In this paper we describe and analyse how this approach can be extended to the direct computation of period doubling bifurcation points. The Newton{Picard scheme is based on shooting and a splitting of the state space in a low-dimensiona...

when the curvature of space is negative (L is the Lobachevskij constant). For obtaining a potential of Newton (or Coulomb) It is necessary to put c2 = −c1/L, L → ∞ (c2 = −c1/R, R → ∞). Let’s consider hereinafter, that at availability of the space curvature to be obliged non-zero, owing to what the Newton potential should be exchanged by a potential (1), in which c2 = −c1/L And to which one actu...

Full Waveform Inversion (FWI) is a powerful seismic imaging method, based on the iterative minimization of the distance between simulated and recorded wavefields. The inverse Hessian operator related to this misfit function plays an important role in the reconstruction scheme. As conventional methods use direct approximations of this operator, we investigate an alternative optimization scheme: ...

Let f be a polynomial of degree at least 2 with coefficients in a number field K, let x0 be a sufficiently general element of K, and let α be a root of f . We give precise conditions under which Newton iteration, started at the point x0, converges v-adically to the root α for infinitely many places v of K. As a corollary we show that if f is irreducible over K of degree at least 3, then Newton ...

The dynamics of rigid bodies coupled by holonomic and non-holonomic constraints are formulated by the Newton Euler method employing a compact notation. The compact notation involves the use of two three by three matrices A and B and the totality of constraint vector C. The Lagrangian and Newton Euler methods are related for a one link rigid body in order to introduce the methodology of the pape...

Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to “lag” the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for some degradation in the convergence rate and robustness. We show that this degradation may be partially mitigated by using the lagged Jacobian as an initial operator in a quasi-Newton method, which...

We present a Newton-CG method for full-waveform seismic inversion. Our method comprises the adjoint-based computation of the gradient and Hessianvector products of the reduced problem and a preconditioned conjugate gradient method to solve the Newton system in matrix-free fashion. A trust-region globalization strategy and a multi-frequency inversion approach are applied. The governing equations...

We study (3+ 1)+D dimensional spacetime, where D extra dimensions are timelike. Compactification of the D timelike dimensions leads to tachyonic Kaluza-Klein gravitons. We calculate the gravitational self-energies of massive spherical bodies due to the tachyonic exchange, discuss their stability, and find that the gravitational force is screened in a certain number of the extra dimensions. We a...

A fast Newton–Krylov algorithm is presented that solves the turbulent Navier–Stokes equations on unstructured 2-D grids. Themodel of Spalart andAllmaras provides the turbulent viscosity and is loosely coupled to themean-flow equations. It is often assumed that the turbulence model must be fully coupled to obtain the full benefit of an inexact Newton algorithm. We demonstrate that a loosely coup...