Multiplicity and structures for traveling wave solutions of the Kuramoto-Sivashinsky equation.
Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes
In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.
Multipoint boundary value problems at resonance
Multiscale analysis of wave propagation in random media. Application to correlation-based imaging
We consider sensor array imaging with the purpose to image reflectors embedded in a medium. Array imaging consists in two steps. In the first step waves emitted by an array of sources probe the medium to be imaged and are recorded by an array of receivers. In the second step the recorded signals are processed to form an image of the medium. Array imaging in a scattering medium is limited because coherent signals recorded at the receiver array and coming from a reflector to be imaged are weak and...
Multiscale deformation analysis by Cauchy-Navier wavelets.
Multiscale expansion and numerical approximation for surface defects⋆
This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic...
Multiscale Finite Element approach for “weakly” random problems and related issues
We address multiscale elliptic problems with random coefficients that are a perturbation of multiscale deterministic problems. Our approach consists in taking benefit of the perturbative context to suitably modify the classical Finite Element basis into a deterministic multiscale Finite Element basis. The latter essentially shares the same approximation properties as a multiscale Finite Element basis directly generated on the random problem. The specific reference method that we use is the Multiscale...
Multiscale finite element coarse spaces for the application to linear elasticity
We extend the multiscale finite element method (MsFEM) as formulated by Hou and Wu in [Hou T.Y., Wu X.-H., A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 1997, 134(1), 169–189] to the PDE system of linear elasticity. The application, motivated by the multiscale analysis of highly heterogeneous composite materials, is twofold. Resolving the heterogeneities on the finest scale, we utilize the linear MsFEM basis for the construction...
Multiscale modelling of sound propagation through the lung parenchyma
In this paper we develop and study numerically a model to describe some aspects of sound propagation in the human lung, considered as a deformable and viscoelastic porous medium (the parenchyma) with millions of alveoli filled with air. Transmission of sound through the lung above 1 kHz is known to be highly frequency-dependent. We pursue the key idea that the viscoelastic parenchyma structure is highly heterogeneous on the small scale ε and use two-scale homogenization techniques to derive effective...
Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy.
Multi-Step Methods are Essentially One-Step Methods.
Multistep methods for coupled second order integro-differential equations: Stability, convergence and error bounds.
Multistep methods for ordinary differential equations with parameters
Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation.
Multivariate approximation theory with -splines
Multivariate Birkhoff-Lagrange interpolation schemes and Cartesian sets of nodes.
Multivariate multiple comparisons with a control in elliptical populations
The approximate upper percentile of Hotelling's T²-type statistic is derived in order to construct simultaneous confidence intervals for comparisons with a control under elliptical populations with unequal sample sizes. Accuracy and conservativeness of Bonferroni approximations are evaluated via a Monte Carlo simulation study. Finally, we explain the real data analysis using procedures derived in this paper.
Multivariate secant method
Multivariate smooth interpolation that employs polyharmonic functions
We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example...
Multivariate spline functions, B-spline bases and polynomial interpolations II