Hunger component is introduced to the existing cockroach swarm optimization (CSO) algorithm to improve its searching ability and population diversity. The original CSO was modelled with three components: chase-swarming, dispersion, and ruthless; additional hunger component which is modelled using partial differential equation (PDE) method is included in this paper. An improved cockroach swarm o...

Although the decomposition method and its modified form were used during the last two decades by many authors to investigate various scientific models, a little attention was devoted for their applications in the field of fluid mechanics. In this paper, the Adomian decomposition method (ADM) is implemented for solving the nonlinear partial differential equation (PDE) describing the peristaltic ...

In this paper, we present a novel image interpolation method based on variational models with both smoothing and orientation constraints. By introducing the orientation constraint, we simplify the nonlinear PDE problem into a series of problems with explicit solutions. In our model, the gradient directions for the interpolated pixels are first estimated using a modified orientation diffusion me...

A major challenge in PDE software is the balance between user-level flexibility and performance on heterogeneous hardware. We discuss our ideas on how this challenge can be tackled, exemplarily for the DUNE framework and in particular its linear algebra and solver components. We demonstrate how the former MPI-only implementation is modified to support MPI+[CPU/GPU] threading and vectorisation. ...

Ebstein's anomaly (EA) is a rare congenital heart disease. Paradoxical embolism (PDE) may occur in EA due to associated atrial septal defect (ASD). An 18 year old male with EA presented with left lower limb ischemia due to PDE to the limb. No features of cerebral embolism was present. PDE is a potential complication of EA. High level of awareness is needed for early diagnosis of PDE in EA to sa...

Numerical method for Cahn-Hilliard equation has been well-studied, but few can be generalized to fractional Cahn-Hilliard equation. In this project to modified the numerical method proposed by Brian Wetton et al in the paper High accuracy solutions to energy gradient flows from material science models[1]. The method they described in the paper is a pseudo-spectral method suitable for considerin...

Twenty-five patients with proven patent ductus arteriosus were examined by pulsed Doppler echocardiography (PDE) before invasive assessment. Ten patients had normal pulmonary artery pressures, and by PDE, pandiastolic ductal flow. Fifteen patients had elevation of mean pulmonary artery pressure, and by PDE, all had abbreviations of diastolic ductal flow. PDE correctly distinguished between pati...

Abstract. The goal of this paper is to develop region based image segmentation algorithms. Two new variational PDE image segmentation models are proposed. The first model is obtained by minimizing an energy function which depends on a modified Mumford-Shah algorithm. The second model is acquired by utilizing prior shape information and region intensity values. The numerical experiments of the p...

In this paper, we present the numerical solution for the PDE-constrained optimization problem arises in cardiac electrophysiology. The monodomain model, which is a well-established model for simulating electrical behavior of the cardiac tissue, appears as the constraint in our problem. Our objective is to search for the optimal applied current, which is able to dampen out the excitation wavefro...

The authors of [Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 6634–6639] proposed sparse Fourier domain approximation of solutions to multiscale PDE problems by soft thresholding. We show here that the method enjoys a number of desirable numerical and analytic properties, including convergence for linear PDEs and a modified equation resulting from the sparse approximation. We also extend the meth...