Search

We propose a smooth fictitious domain/multiresolution method for enhancing the accuracy order in solving second order elliptic partial differential equations on general bivariate domains. We prove the existence and uniqueness of the solution of a corresponding discrete problem and a so-called interior error estimate which justifies the improved accuracy order. Numerical experiments are conducted on a Cassini oval. [ABSTRACT FROM AUTHOR]

This work is devoted to the definition, the analysis and the implementation in the univariate case of a new numerical method for the approximation of partial differential equations solutions defined on complex domains. It couples a smooth fictitious domain method derived in Haslinger et al. (Numer Linear Algebra 14:713-739, ) with multiscale approximations. After the definition of the method, error estimates are derived: they allow to control a global error (on the whole domain including the boundary of the initial complex domain) as well as an interior error (for any sub-domain strictly included in the control domain). Numerical implementation and tests on univariate elliptic problems are finally described. [ABSTRACT FROM AUTHOR]

A new nonlinear representation of multiresolution decompositions and new thresholding adapted to the presence of discontinuities are presented and analyzed. They are based on a nonlinear modification of the multiresolution details coming from an initial (linear or nonlinear) scheme and on a data dependent thresholding. Stability results are derived. Numerical advantages are demonstrated on various numerical experiments. [ABSTRACT FROM AUTHOR]

A nonlinear multiresolution scheme within Harten's framework is presented, based on a new nonlinear, centered piecewise polynomial interpolation technique. Analytical properties of the resulting subdivision scheme, such as convergence, smoothness, and stability, are studied. The stability and the compression properties of the associated multiresolution transform are demonstrated on several numerical experiments on images. [ABSTRACT FROM AUTHOR]