The Laplace transform analytic element method (LT-AEM), applies the traditionally steady-state analytic element method (AEM) to the Laplace-transformed diffusion equation (Furman and Neuman, 2003). This strategy preserves the accuracy and elegance of the AEM while extending the method to transient phenomena. The approach taken here utilizes eigenfunction expansion to derive analytic solutions to the modified Helmholtz equation, then back-transforms the LT-AEM results with a numerical inverse Laplace transform algorithm. The two-dimensional elements derived here include the point, circle, line segment, ellipse, and infinite line, corresponding to polar, elliptical and Cartesian coordinates. Each element is derived for the simplest useful case, an impulse response due to a confined, transient, single-aquifer source. The extension of these elements to include effects due to leaky, unconfined, multi-aquifer, wellbore storage, and inertia is shown for a few simple elements (point and line), with ready extension to other elements. General temporal behavior is achieved using convolution between these impulse and general time functions; convolution allows the spatial and temporal components of an element to be handled independently.
The Laplace transform analytic element method (LT-AEM), applies the traditionally steady-state analytic element method (AEM) to the Laplace-transformed diffusion equation (Furman and Neuman, 2003). This strategy preserves the accuracy and elegance of the AEM while extending the method to transient phenomena. The approach taken here utilizes eigenfunction expansion to derive analytic solutions to the modified Helmholtz equation, then back-transforms the LT-AEM results with a numerical inverse Laplace transform algorithm. The two-dimensional elements derived here include the point, circle, line segment, ellipse, and infinite line, corresponding to polar, elliptical and Cartesian coordinates. Each element is derived for the simplest useful case, an impulse response due to a confined, transient, single-aquifer source. The extension of these elements to include effects due to leaky, unconfined, multi-aquifer, wellbore storage, and inertia is shown for a few simple elements (point and line), with ready extension to other elements. General temporal behavior is achieved using convolution between these impulse and general time functions; convolution allows the spatial and temporal components of an element to be handled independently.
Basic Results.- Inversion Formulae and Practical Results.- The Method of Series Expansion.- Quadrature Methods.- Rational Approximation Methods.- The Method of Talbot.- Methods based on the...
This book is designed to cater the needs of the under graduate science and engineering students. It contains with the fundamental concepts related to Laplace Transformation and Inverse Laplace...
The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and...
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