Noticias en español
DIMENSIONALLY ADAPTIVE METHODS (DAM) FOR THE SIMULATION AND INVERSION OF ELECTROMAGNETIC GEOPHYSICAL MEASUREMENTS
ABSTRACT A number of three dimensional (3D) simulators of geophysical logging measurements have been developed during the last two decades for oil-industry applications. These simulators have been suc- cessfully used to study and quantify different physical effects occurring in 3D geometries. Despite such recent advances, there are still many 3D effects for which reliable simulations are not available. Furthermore, in most of the existing results, only partial validations have been reported, typically obtained by comparing solutions of simplified model problems against the corresponding...
Read MoreThe Generalized Riemann problem as a building block for high-order finite volume methods}
Abstract The Godunov theorem provides a limitation for finite volume schemes, linear and monotone; only first order of accuracy can be achieved. A family of non-linear schemes, called ADER (Arbitrary accuracy DERivative Riemann problems), attempting to circumvent Godunov’s theorem, has been proposed. Building block for these schemes are: the polynomial reconstruction of cell averages and; the solution of special Cauchy problem, the so called generalized Riemann problems. The reconstruction and the solution of Generalized Riemann problems allow us to construct schemes of accuracy $p...
Read MoreThe Generalized Riemann problem as a building block for high-order finite volume methods
Abstract The Godunov theorem provides a limitation for finite volume schemes, linear and monotone; only first order of accuracy can be achieved. A family of non-linear schemes, called ADER (Arbitrary accuracy DERivative Riemann problems), attempting to circumvent Godunov’s theorem, has been proposed. Building block for these schemes are: the polynomial reconstruction of cell averages and; the solution of special Cauchy problem, the so called generalized Riemann problems. The reconstruction and the solution of Generalized Riemann problems allow us to construct schemes of accuracy p >...
Read MoreModels of tumor growth and therapy
Abstract: Models of tumor growth are now commonly used to predict the evolution of cancers, based on images for instance. These models serve to predict the evolution of the disease in medical treatments, to understand the biological effects that permit tumor growth and decide of the optimal therapy. A more recent subject is to explain emergence of resistance to drug and its implication in therapeutic failures. These models contain several levels of complexity, both in terms of the biological and mechanical effects, and therefore in their math- ematical description. The number of scales, from...
Read MoreSimulation and inversion of resistivity and sonic logging measurements for the characterization of the Earth’s Subsurface
A number of 3D simulators of borehole logging measurements have been developed during the last two decades for oil-industry applications. These simulators have been successfully used to study and quantify different physical effects occurring in 3D geometries. Despite such recent advances, there are still many 3D effects for which reliable simulations are not available. Furthermore, in most of the existing results only partial validations have been reported, typically obtained by comparing solutions of simplified model problems against the corresponding solutions calculated with a lower...
Read MoreControl and numerical simulation in large time horizons
ABSTRACT: In this talk we present some aspects of our work in Partial Differential Equations, their control and numerical approximation focusing on topics relevant for the 2013 program of Mathematics of Planet Earth. One of the main distinguishing aspects of climate science is that evolving phenomena have to be understood in a long time horizon. In this lecture we shall analyze this issue from viewpoints. First of all, following a recent joint work with A. Porretta, we will address the problem of large time versus steady state control. The problem we consider is as follows. Assume that the...
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