Finite element solution for elliptic partial differential equations

The contents of this thesis are a detailed study of the implementation of Finite Element method for solving linear and non-linear elliptic partial differential equations. It commences with a description and classification of partial differential equations, the related matrix and eigenvalue theory and the related matrix methods to solve the linear and non-linear systems of equations. In Chapter Three, we discuss the development of the, finite element method and its application with a full description of an orderly step-by-step process. In Chapter Four, we discuss the implementation of developing an efficient easy-to-use finite element program for the general two-dimensional problem along with the capability of handling problems for different domains and boundary conditions and with a fully automated mesh generation and refinement technique along with a description of generalised pre- and post-processors for the Finite Element Method. [Continues.

Lane marking detection using simple encode decode deep learning technique: SegNet

In recent times, many innocent people are suffering from sudden death for the sake of unwanted road accidents, which also riveting a lot of financial properties. The researchers have deployed advanced driver assistance systems (ADAS) in which a large number of automated features have been incorporated in the modern vehicles to overcome human mortality as well as financial loss, and lane markings detection is one of them. Many computer vision techniques and intricate image processing approaches have been used for detecting the lane markings by utilizing the handcrafted with highly specialized features. However, the systems have become more challenging due to the computational complexity, overfitting, less accuracy, and incapability to cope up with the intricate environmental conditions. Therefore, this research paper proposed a simple encode-decode deep learning model to detect lane markings under the distinct environmental condition with lower computational complexity. The model is based on SegNet architecture for improving the performance of the existing researches, which is trained by the lane marking dataset containing different complex environment conditions like rain, cloud, low light, curve roads. The model has successfully achieved 96.38% accuracy, 0.0311 false positive, 0.0201 false negative, 0.960 F1 score with a loss of only 1.45%, less overfitting and 428 ms per step that outstripped some of the existing researches. It is expected that this research will bring a significant contribution to the field lane marking detection

An efficient encode-decode deep learning network for lane markings instant segmentation

Nowadays, advanced driver assistance systems (ADAS) has been incorporated with a distinct type of progressive and essential features. One of the most preliminary and significant features of the ADAS is lane marking detection, which permits the vehicle to keep in a particular road lane itself. It has been detected by utilizing high-specialized, handcrafted features and distinct post-processing approaches lead to less accurate, less efficient, and high computational framework under different environmental conditions. Hence, this research proposed a simple encode-decode deep learning approach under distinguishing environmental effects like different daytime, multiple lanes, different traffic condition, good and medium weather conditions for detecting the lane markings more accurately and efficiently. The proposed model is emphasized on the simple encode-decode Seg-Net framework incorporated with VGG16 architecture that has been trained by using the inequity and cross-entropy losses to obtain more accurate instant segmentation result of lane markings. The framework has been trained and tested on a vast public dataset named Tusimple, which includes around 3.6K training and 2.7 k testing image frames of different environmental conditions. The model has noted the highest accuracy, 96.61%, F1 score 96.34%, precision 98.91%, and recall 93.89%. Also, it has also obtained the lowest 3.125% false positive and 1.259% false-negative value, which transcended some of the previous researches. It is expected to assist significantly in the field of lane markings detection applying deep neural networks