An implicit integration strategy was developed and implemented for use with the material point method (MPM). An incremental-iterative solution strategy was developed around Newton’s method to solve the equations of motion with Newmark integration to update the kinematic variables. Test problems directly compared the implicit MPM solutions with those obtained using an explicit MPM code and impli...

This paper investigates the expected benefits of the implicit time integration scheme in the solution of jointed rock problems. Discontinuous Deformation Analyses (DDA) exploits the unconditional stability of the implicit time integration scheme, and allows the time step size of the solution to be much larger than the critical time step size dictated by the stability requirement of the explicit...

Behavioral, neuropsychological, and neuroimaging evidence indicate categories can be learned either via an explicit rule-based mechanism dependent on medial temporal and prefrontal brain regions, or via an implicit information integration mechanism relying on the basal ganglia and occipital cortex. In this study, participants viewed Gabor patches that varied on two dimensions, and learned categ...

This paper establishes a link between the stability of a first order, explicit discrete event integration scheme and the stability criteria for the explicit Euler method. The paper begins by constructing a time-varying linear system with bounded inputs that is equivalent to the first order discrete event integration scheme. The stability of the discrete event system is shown to result from the ...

analysis of time series data can involve the inversion of large covariance matrices. for theclass of arma (p, q) processes there are no exact explicit expressions for these inverses, except for thema (1) process. in practice, the sample covariance matrix can be very large and inversion can becomputationally time consuming and so approximate explicit expressions for the inverse are desirable.thi...