We present a survey of the fundamentals and the applications of sparse grids, with a focus
on the solution of partial differential equations (PDEs). The sparse grid approach, introduced …

Universitext is a series of textbooks that presents material from a wide variety of
mathematical disciplines at master's level and beyond. The books, often well class-tested by …

The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

The technique of sparse grids allows to overcome the curse of dimensionality, which
prevents the use of classical numerical discretization schemes in more than three or four …

The efficient numerical treatment of high dimensional problems is hampered by the curse of
dimensionality. We review approximation techniques which overcome this problem to some …

A major challenge in computational finance is the pricing of options that depend on a large
number of risk factors. Prominent examples are basket or index options where dozens or …

The multi-dimensional Black–Scholes equation is solved numerically for a European call
basket option using a priori–a posteriori error estimates. The equation is discretized by a …

In this paper, we consider the discretization in space and time of parabolic differential
equations where we use the so-called space-time sparse grid technique. It employs the …

The accurate numerical solution of partial differential equations (PDEs) is a central task in
numerical analysis allowing to model a wide range of natural phenomena by employing …

Diese Arbeit befasst sich mit Dünngitterverfahren zur Lösung von höherdimensionalen
Problemen. Sie zeigt drei neue Aspekte von Dünnen Gittern auf: Erweiterungen der …