[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-114417-en":3,"doc-seo-114417-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},114417,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",6,"Technology","Numerical Electrostatics Using MATLAB - Lawrence N Dworsky","Numerical Electrostatics Using MATLAB presents a practical, computation-focused approach to electrostatics, starting from core concepts such as charge, electric fields, Gauss’s law, potential, energy storage, and the governing Poisson/Laplace formulations. It then develops and applies multiple numerical techniques—Method of Moments, Finite Difference Method, and Finite Element Method—showing how to set up equations, build meshes, handle dielectric interfaces and symmetries, and compute voltages, fields, and charge distributions. Includes example modeling workflows, resolution limits, and extensions to multi-electrode systems, probabilistic potential theory, and electrostatic forces.","Contents  \nCover  \nTitle page  \nCopyright page  \nPreface  \nIntroduction  \nAcknowledgments  \n1 A Review of Basic Electrostatics  \n1.1 Charge, Force, and the Electric Field  \n1.2 Electric Flux Density and Gauss’s Law  \n1.3 Conductors  \n1.4 Potential, Gradient, and Capacitance  \n1.5 Energy in the Electric Field  \n1.6 Poisson’s and Laplace’s Equations  \n1.7 Dielectric Interfaces  \n1.8 Electric Dipoles  \n1.9 The Case for Approximate Numerical Analysis  \nProblems  \n2 The Uses of Electrostatics  \n2.1 Basic Circuit Theory  \n2.2 Radio Frequency Transmission Lines  \n2.3 Vacuum Tubes and Cathode Ray Tubes  \n2.4 Field Emission and the Scanning Electron Microscope  \n2.5 Electrostatic Force Devices  \n2.6 Gas Discharges and Lighting Devices  \n3 Introduction to the Method of Moments Technique for Electrostatics  \n3.1 Fundamental Equations  \n3.2 A Working Equation Set  \n3.3 The Single-Point Approximation for Off-Diagonal Terms  \n3.4 Exact Solutions for the Diagonal Term and In-Plane Terms  \n3.5 Approximating Li,j  \nProblems  \n4 Examples Using the Method of Moments  \n4.1 A First Modeling Program  \n4.2 Input Data File Preparation for the First Modeling Program  \n4.3 Processing the Input Data  \n4.4 Generating the Li,j Array  \n4.5 Solving the System and Examining Some Results  \n4.6 Limits of Resolution  \n4.7 Voltages and Fields  \n4.8 Varying the Geometry  \nProblems  \n5 Symmetries, Images, and Dielectrics  \n5.1 Symmetries  \n5.2 Images  \n5.3 Multiple Images and the Symmetric Stripline  \n5.4 Dielectric Interfaces  \n5.5 Two-Dimensional Cross Sections of Uniform ThreeDimensional Structures  \n5.6 Charge Profiles and Current Bunching  \n5.7 Cylinder Between Two Planes  \nProblems  \n6 Triangles  \n6.1 Introduction to Triangular Cells  \n6.2 Right Triangles  \n6.3 Calculating Li,i(Self) Coefficients  \n6.4 Calculating Li,j FOR i ≠j  \n6.5 Basic Meshing and Data Formats for Triangular Cell MoM Programs  \n6.6 Using MATLAB to Generate Triangular Meshings  \n6.7 Calculating Voltages  \n6.8 Calculating the Electric Field  \n6.9 Three-Dimensional Structures  \n6.10 Charge Profiles  \nProblems  \n7 Summary and Overview  \n7.1 Where We Were, Where We’re Going  \n8 The Finite Difference Method  \n8.1 Introduction and a Simple Example  \n8.2 Setting up and Solving a Basic Problem  \n8.3 The Gauss–Seidel (Relaxation) Solution Technique  \n8.4 Charge, Gauss’s Law, and Resolution  \n8.5 Voltages and Fields  \n8.6 Stored Energy and Capacitance  \nProblems  \n9 Refining the Finite Difference Method  \n9.1 Refined Grids  \n9.2 Arbitrary Conductor Shapes  \n9.3 Mixed Dielectric Regions and a New Derivation of the Finite Difference Equation  \n9.4 Example: Structure with a Dielectric Interface  \n9.5 Axisymmetric Cylindrical Coordinates  \n9.6 Symmetry Boundary Condition  \n9.7 Duality, and Upper and Lower Bounds to Solutions for Transmission Lines  \n9.8 Extrapolation  \n9.9 Three-Dimensional Grids  \nProblems  \n10 Multielectrode Systems  \n10.1 Multielectrode Structures  \n10.2 Utilizing Superposition  \n10.3 Utilizing Symmetry  \n10.4 Circuital Relations and a Caveat  \n10.5 Floating Electrodes  \nProblems  \n11 Probabilistic Potential Theory  \n11.1 Random Walks and the Diffusion Equation  \n11.2 Voltage at a Point from Random Walks  \n11.3 Diffusion  \n11.4 Variable-Step-Size Random Walks  \n11.5 Three-Dimensional Structures  \nProblems  \n12 The Finite Element Method (FEM)  \n12.1 Introduction  \n12.2 Solving Laplace’s Equation by Minimizing Stored Energy  \n12.3 A Simple One-Dimensional Example  \n12.4 AVery Simple Finite Element Approximation  \n12.5 Arbitrary Number of Lines Approximation  \n12.6 Mixed Dielectrics  \n12.7 A Quadratic Approximation  \n12.8 A Simple Two-Dimensional FEM Program Problems  \n13 Triangles and Two-Dimensional Unstructured Grids  \n13.1 Introduction  \n13.2 Aside: The Area of a Triangle  \n13.3 The Coefficient Matrix  \n13.4 A Simple Example  \n13.5 A Two-Dimensional Triangular Mesh Program Problems  \n14 A Zoning System and Some Examples  \n14.1 General Introduction  \n14.2 Introduction to gmsh  \n14.3","cbCaio7q2JeXtLsu","https://ap.wps.com/l/cbCaio7q2JeXtLsu","pdf",17489527,2,1,676,"English","en",105,"# A Review of Basic Electrostatics\n## Charge, Force, and the Electric Field\n## Electric Flux Density and Gauss’s Law\n## Conductors\n## Potential, Gradient, and Capacitance\n## Energy in the Electric Field\n## Poisson’s and Laplace’s Equations\n## Dielectric Interfaces\n## Electric Dipoles\n## The Case for Approximate Numerical Analysis\n# The Uses of Electrostatics\n## Basic Circuit Theory\n## Radio Frequency Transmission Lines\n## Vacuum Tubes and Cathode Ray Tubes\n## Field Emission and the Scanning Electron Microscope\n## Electrostatic Force Devices\n## Gas Discharges and Lighting Devices\n# Introduction to the Method of Moments Technique for Electrostatics\n## Fundamental Equations\n## A Working Equation Set\n## The Single-Point Approximation for Off-Diagonal Terms\n## Exact Solutions for the Diagonal Term and In-Plane Terms\n## Approximating Li,j\n# Examples Using the Method of Moments\n## A First Modeling Program\n## Input Data File Preparation for the First Modeling Program\n## Processing the Input Data\n## Generating the Li,j Array\n## Solving the System and Examining Some Results\n## Limits of Resolution\n## Voltages and Fields\n## Varying the Geometry\n# Symmetries, Images, and Dielectrics\n## Symmetries\n## Images\n## Multiple Images and the Symmetric Stripline\n## Dielectric Interfaces\n## Two-Dimensional Cross Sections of Uniform Three-Dimensional Structures\n## Charge Profiles and Current Bunching\n## Cylinder Between Two Planes\n# Triangles\n## Introduction to Triangular Cells\n## Right Triangles\n## Calculating Li,i(Self) Coefficients\n## Calculating Li,j FOR i ≠ j\n## Basic Meshing and Data Formats for Triangular Cell MoM Programs\n## Using MATLAB to Generate Triangular Meshings\n## Calculating Voltages\n## Calculating the Electric Field\n## Three-Dimensional Structures\n## Charge Profiles","[{\"question\":\"What foundational electrostatics topics does the book cover before introducing numerical methods?\",\"answer\":\"It reviews charge and the electric field, Gauss’s law, conductors, potential and capacitance, energy in the electric field, and Poisson/Laplace equations, including dielectric interfaces and electric dipoles.\"},{\"question\":\"How does the book approach electrostatics numerically using the Method of Moments?\",\"answer\":\"It introduces the MoM fundamental equations and a working equation set, explains approximations for off-diagonal terms, derives exact components, and shows how to generate and solve the Li,j array through a modeling program.\"},{\"question\":\"What numerical techniques beyond MoM are presented, and what do they compute?\",\"answer\":\"The book presents the Finite Difference Method and the Finite Element Method, refining grids and handling mixed dielectrics and symmetries to compute voltages, electric fields, charge distributions, and stored energy/capacitance.\"}]",1785399579,1704,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"numerical-electrostatics-using-matlab-lawrence-n-dworsky","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/technology/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/numerical-electrostatics-using-matlab-lawrence-n-dworsky/114417/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-08-01","2026-07-30",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What foundational electrostatics topics does the book cover before introducing numerical methods?","Question",{"text":75,"@type":76},"It reviews charge and the electric field, Gauss’s law, conductors, potential and capacitance, energy in the electric field, and Poisson/Laplace equations, including dielectric interfaces and electric dipoles.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the book approach electrostatics numerically using the Method of Moments?",{"text":80,"@type":76},"It introduces the MoM fundamental equations and a working equation set, explains approximations for off-diagonal terms, derives exact components, and shows how to generate and solve the Li,j array through a modeling program.",{"name":82,"@type":73,"acceptedAnswer":83},"What numerical techniques beyond MoM are presented, and what do they compute?",{"text":84,"@type":76},"The book presents the Finite Difference Method and the Finite Element Method, refining grids and handling mixed dielectrics and symmetries to compute voltages, electric fields, charge distributions, and stored energy/capacitance.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,113,118,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & 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