Automatic differentiation is a popular technique for computing derivatives of computer
programs. While automatic differentiation has been successfully used in countless …

A moving discontinuous Galerkin finite element method with interface condition enforcement
is formulated for flows with discontinuous interfaces. The underlying weak formulation …

THIS paper contains a complete formulation of the continuous adjoint approach for the
shape optimization of an obstacle with a boundary S immersed in a fluid governed by the …

Automatic differentiation, also known as backpropagation, AD, autodiff, or algorithmic
differentiation, is a popular technique for computing derivatives of computer programs. While …

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for
immiscible two-phase flows, eg air and water, which is widely used in marine engineering …

Recent research has used deep learning to develop partial differential equation (PDE)
models in science and engineering. The functional form of the PDE is determined by a …

This paper continues the convergence analysis in [M. Giles and S. Ulbrich, SIAM J. Numer.
Anal., 48 (2010), pp. 882–904] of discrete approximations to the linearized and adjoint …

In this chapter we survey recent progress on mathematical results on gas flow in pipe
networks with a special focus on questions of control and stabilization. We briefly present the …

This paper reports on the derivation and implementation of a shape optimization procedure
for the minimization of hemolysis induction in blood flows through biomedical devices …

In this paper, we discuss the efficiency of various numerical methods for the inverse design
of the Burgers equation, both in the viscous and in the inviscid case, in long time-horizons …