“Colonel Tiso’s experience with operational planning and combat service with multinational forces in Iraq provides an exceptional background for this riveting, exciting, and most interesting book that superbly captures the challenges of Coalition Warfare.” — Lieutenant General (Retired) Joseph W. Kinzer, USA The decision to not deploy reoriented, trained Iraqi divisions and other allied forces in numbers significant enough to adequately stabilize the situation in Iraq in 2003–04 resulted in significant shortages of manpower and equipment that eventually led to a less-than-satisfactory ending to the campaign, and significantly challenged the entire Coalition effort in the first year of Operation Iraqi Freedom. The roles and missions assumed by allies were vitally important in the under-resourced effort to bring order to the chaos of Iraq but would remain relatively unheralded throughout most of the campaign. Colonel Tiso’s account of this time offers unique insights into the challenges of planning the Iraqi campaign and the intricacies and challenges of multinational service through the lens of his assignments as a war planner at U.S. Central Command, Senior Military Adviser of the Arab Peninsula Shield Force and the Polish-led Multinational Division (Central-South), and Chief of Staff and Deputy Chief of Staff for Operations (C-3) of the Coalition Military Assistance Training Team tasked to develop the New Iraqi Army. His observations cast significant light on the missions these units undertook and the challenges they confronted. His firsthand account of operational planning for war in Iraq captures the concerns of the military planners and senior commanders to liberate and stabilize the country, enabling the reader to better understand the challenges of operational war planning, coalition warfare, the difficulty of stabilizing Iraq after the fall of Baghdad, the development of the New Iraqi Army, and ultimately a deeper understanding of America’s “long war” in Iraq.
This thesis is concerned with the numerical solution of boundary value problems (BVPs) governed by nonlinear elliptic partial differential equations (PDEs). To iteratively solve such BVPs, it is of primal importance to develop efficient schemes that guarantee convergence of the numerically approximated PDE solutions towards the exact solution. The new adaptive wavelet theory guarantees convergence of adaptive schemes with fixed approximation rates. Furthermore, optimal, i.e., linear, complexity estimates of such adaptive solution methods have been established. These achievements are possible since wavelets allow for a completely new perspective to attack BVPs: namely, to represent PDEs in their original infinite dimensional realm. Wavelets in this context represent function bases with special analytical properties, e.g., the wavelets considered herein are piecewise polynomials, have compact support and norm equivalences between certain function spaces and the $ell_2$ sequence spaces of expansion coefficients exist. This theoretical framework is implemented in the course of this thesis in a truly dimensionally unrestricted adaptive wavelet program code, which allows one to harness the proven theoretical results for the first time when numerically solving the above mentioned BVPs. Numerical studies of 2D and 3D PDEs and BVPs demonstrate the feasibility and performance of the developed schemes. The BVPs are solved using an adaptive Uzawa algorithm, which requires repeated solution of nonlinear PDE sub-problems. This thesis presents for the first time a numerically competitive implementation of a new theoretical paradigm to solve nonlinear elliptic PDEs in arbitrary space dimensions with a complete convergence and complexity theory.
“Colonel Tiso’s experience with operational planning and combat service with multinational forces in Iraq provides an exceptional background for this riveting, exciting, and most interesting book that superbly captures the challenges of Coalition Warfare.” — Lieutenant General (Retired) Joseph W. Kinzer, USA The decision to not deploy reoriented, trained Iraqi divisions and other allied forces in numbers significant enough to adequately stabilize the situation in Iraq in 2003–04 resulted in significant shortages of manpower and equipment that eventually led to a less-than-satisfactory ending to the campaign, and significantly challenged the entire Coalition effort in the first year of Operation Iraqi Freedom. The roles and missions assumed by allies were vitally important in the under-resourced effort to bring order to the chaos of Iraq but would remain relatively unheralded throughout most of the campaign. Colonel Tiso’s account of this time offers unique insights into the challenges of planning the Iraqi campaign and the intricacies and challenges of multinational service through the lens of his assignments as a war planner at U.S. Central Command, Senior Military Adviser of the Arab Peninsula Shield Force and the Polish-led Multinational Division (Central-South), and Chief of Staff and Deputy Chief of Staff for Operations (C-3) of the Coalition Military Assistance Training Team tasked to develop the New Iraqi Army. His observations cast significant light on the missions these units undertook and the challenges they confronted. His firsthand account of operational planning for war in Iraq captures the concerns of the military planners and senior commanders to liberate and stabilize the country, enabling the reader to better understand the challenges of operational war planning, coalition warfare, the difficulty of stabilizing Iraq after the fall of Baghdad, the development of the New Iraqi Army, and ultimately a deeper understanding of America’s “long war” in Iraq.
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