DPSM for Modeling Engineering Problems

The first book on DPSM—a patented new technology that is superior for solving/modeling engineering problems
In the last few decades, numerical methods like Finite Element Method (FEM) and Boundary Element Method (BEM) have been used for solving a variety of engineering problems in bounded and unbounded geometries, but they are not interchangeable across homogeneous and inhomogeneous media and encounter difficulties at high frequencies. Now, Distributed Point Source Method (DPSM) has been developed for solving ultrasonic, magnetic, electrostatic, and electromagnetic engineering problems with a single, unified technique.
In DPSM—unlike FEM and BEM—it is not necessary to discretize or mesh the problem geometry or its boundary. Instead, point sources are placed near the boundaries and interfaces to build a model that can correctly take into account the radiation and continuity conditions at these interfaces, making it a faster and more versatile method than the conventional numerical techniques.
Valuable for graduate students and engineers in research and development, this book covers basic and advanced theories and applications of DPSM and includes a User′s Manual for the DPSM–based computer program.

Spis treści:
Chapter 1. Basic Theory of Distributed Point Source Method (DPSM) and its Application to Some Simple Problems (D. Placko and T. Kundu).
1.1 Introduction and Historical Development of DPSM.
1.2 Basic Principles of DPSM Modeling.
1.2.1 The fundamental idea.
1.2.1.1 Basic equations.
1.2.1.2 Boundary conditions.
1.2.2 Example in the case of a magnetic open core sensor.
1.2.2.1 Governing equations and solution.
1.2.2.2 Solution of coupling equations.
1.2.2.3 Results and discussion.
1.3 Examples from Ultrasonic Transducer Modeling.
1.3.1 Justification of modeling a finite plane source by a distribution of point sources .
1.3.2 Planar piston transducer in a flu id.
1.3.2.1 Conventional surface integral technique.
1.3.2.2 Alternative distributed point source method (DPSM) for computing the ultrasonic field.
1.3.2.2.1 Matrix formulation.
1.3.2.3 Restrictions on rS for point source distribution.
1.3.3 Focused transducer in a homogeneous fluid.
1.3.4 Ultrasonic field in a non–homogeneous fluid in presence of an interface.
1.3.4.1 Pressure field computation in fluid 1 at point P.
1.3.4.2 Pressure field computation in fluid 2 at point Q.
1.3.5 DPSM technique for ultrasonic field modeling in non–homogeneous fluid.
1.3.5.1 Field computation in fluid 1.
1.3.5.1.1 Approximations in computing the field.
1.3.5.2 Field in fluid 2.
1.3.6 Ultrasonic field in presence of a scatterer.
1.3.7 Numerical results.
1.3.7.1 Ultrasonic field in a homogeneous fluid.
1.3.7.2 Ultrasonic field in a non–homogeneous fluid – DPSM technique.
1.3.7.3 Ultrasonic field in a non–homogeneous fluid – surface integral method.
1.3.7.4 Ultrasonic field in presence of a finite size scatterer.
References.
Chapter 2. Advanced Theory of DPSM – Modeling Multi–Layered Medium and Inclusions of Arbitrary Shape (T. Kundu and D. Placko).
2.1 Introduction.
2.2 Theory of Multi–Layered Medium Modeling.
2.2.1 Transducer faces not coinciding with any interface.
2.2.1.1 Source strength determination from boundary and interface conditions.
2.2.2 Transducer faces coinciding with the interface – Case 1: Transducer faces modeled separately.
2.2.2.1 Source strength determination from interface and boundary conditions.
2.2.2.2 Counting number of equations and number of unknowns.
2.2.3 Transducer faces coinciding with the interface – Case 2: Transducer faces are part of the interface.
2.2.3.1 Source strength determination from interface and boundary conditions.
2.2.4 Special case involving one interface and one transducer onl y.
2.3 Theory for Multi–layered Medium Considering the Interaction Effect on the Transducer Surface .
2.3.1 Source strength determination from interface conditions.
2.3.2 Counting number of equations and number of unknowns.
2.4 Interference between two Transducers: Step–by–Step Analysis of Multiple Reflection.
2.5 Scattering by an Inclusion of Arbitrary Shape.
2.6 Scattering by an Inclusion of Arbitrary Shape – An Alternative Approach.
2.7 Electric Field in a Multi–Layered Medium.
2.8 Ultrasonic Field in a Multi–Layered Fluid Medium.
2.8.1 Ultrasonic field developed in a three–layered medium.
2.8.2 Ultrasonic field developed in a four–layered fluid medium.
References.
Chapter 3. Ultrasonic Modeling in Fluid Media (T. Kundu, R. Ahmad, N. Alnuaimi and D. Placko).
3.1 Introduction.
3.2 Primary and Secondary Sources.
3.3 Modeling Ultrasonic Transducers of Finite Dimension Immersed in a Homogeneous Fluid.
3.3.1 Numerical results – ultrasonic transducers of finite dimension immersed in fluid.
3.4 Modeling Ultrasonic Transducers of Finite Dimension Immersed in a Non–Homogeneous Fluid.
3.4.1 Obtaining the strengths of active and passive source layers.
3.4.1.1 Computation of the source strength vectors when multiple reflection between the transducer and the interface are ignored.
3.4.1.2 Computation of the source strength vectors considering the interaction effects between the transducer and the interface .
3.4.2 Numerical results – ultrasonic transducer immersed in non–homogeneous fluid.
3.5 Reflection at a Fluid–Solid Interface – Ignoring Multiple Reflections between the Transducer Surface and the Interface.
3.5.1 Numerical results for fluid–solid interface.
3.6 Modeling Ultrasonic Field in Presence of a Thin Scatterer of Finite Dimension.
3.7 Modeling Ultrasonic Field inside a Multi–Layered Fluid Medium.
3.8 Modeling Phased–Array Transducers Immersed in a Fluid.
3.8.1 Description and use of phased array transducers.
3.8.2 Theory of phased array transducer modeling.
3.8.3 Dynamic focusing and time lag determination.
3.8.4 Interaction between two transducers in a homogeneous fluid .
3.8.5 Numerical results for phased array transducer modeling.
3.8.5.1 Dynamic steering and focusing.
3.8.5.2 Interaction between two phased array transducers placed face to face.
Reference.
Chapter 4. Advanced Applications of Distributed Point Source Method – Ultrasonic Field Modeling in Solid Media (S. Banerjee and T. Kundu).
4.1 Introduction.
4.2 Calculation of Displacement and Stress Green’s Functions in Solids.
4.2.1 Point source excitation in a solid.
4.2.2 Calculation of displacement Green’s function.
4.2.3 Calculation of stress Green’s function.
4.3 Elemental Point Source in a Solid.
4.3.1 Displacement and stress Green’s functions.
4.3.2 Differentiation of displacement Green’s function with respect to x1, x2, x3.
4.3.3 Computation of displacements and stresses in the solid for multiple point sources.
4.3.4 Matrix representation.
4.4 Calculation of Pressure and Displacement Green’s Functions in the Fluid Adjacent to the Solid Half–Space.
4.4.1 Displacement and potential Green’s functions in the fluid.
4.4.2 Computation of displacement and pressure in the fluid.
4.4.3 Matrix representation.
4.5 Application 1: Ultrasonic Field Modeling near Fluid–Solid Interface [Banerjee et al. 2006].
4.5.1 Matrix formulation to calculate source strengths.
4.5.2 Boundary conditions.
4.5.3 Solution.
4.5.4 Numerical results on ultrasonic field modeling near fluid–solid interface.
4.6 Application 2: Ultrasonic Field Modeling in a Solid Plate [Banerjee and Kundu 2006a].
4.6.1 Ultrasonic field modeling in a homogeneous sol