Forward and reverse modes of algorithmic differentiation (AD) transform implementations of multivariate vector functions F : IR → IR as computer programs into tangent and adjoint code, respectively. The adjoint mode is of particular interest in large-scale functions due to the independence of its computational cost on the number of free variables. The additional memory requirement for the compu...

This paper presents a fast method that computes deformations with fracturing of an object using a hierarchical lattice. Our method allows numerically stable computation based on so-called shape matching. During the simulation, the deformed shape of the object and the condition of fracturing are used to determine the appropriate detail level in the hierarchy of the lattices. Our method modifies ...

This paper describes triaxial compression tests conducted to determine the effect of fiber inclusion on stiffness and deformation characteristics of sand-gravel mixtures. Tested soil was a mixture of Babolsar sand from the shores of the Caspian Sea and Karaj River gravel. Portland cement was used as the cementing agent and fibers 12mm in length and 0.023mm in diameter at 0%, 0.5% and 1.0% were ...

In this work, algorithmicmodifications are proposed and analyzed for a recently developed stabilized finite strain Discontinuous Galerkin (DG) method. The distinguishing feature of the original method, referred to as VMDG, is a consistently derived expression for the numerical flux and stability tensor that account for evolving material and geometric nonlinearity in the vicinity of the interfac...

We consider the Algorithmic Differentiation (also know as Automatic Differentiation; AD) of numerical simulation programs that contain calls to direct solvers for systems of n linear equations. AD of the linear solvers yields a local overhead of O(n) for the computation of directional derivatives or adjoints of the solution vector with respect to the system matrix and right-hand side. The local...

In this paper temporal local tangent space alignment is proposed to deal with time-dependent data, such as video and motion capture data. It is an extension of local tangent space alignment, for short, LTSA, from spacial to temporal learning. LTSA is a nonlinear dimension reduction method based on Euclidean distance. Temporal LTSA, however, is dependent on the continuity of time of input data. ...