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Multiphysics
In computational modelling, multiphysics simulation (often shortened to simply "multiphysics") is defined as the simultaneous simulation of different aspects of a physical system or systems and the interactions among them. For example, simultaneous simulation of the physical stress on an object, the temperature distribution of the object and the thermal expansion which leads to the variation of the stress and temperature distributions would be considered a multiphysics simulation. Multiphysics simulation is related to multiscale simulation, which is the simultaneous simulation of a single process on either multiple time or distance scales. As an interdisciplinary field, multiphysics simulation can span many science and engineering disciplines. Simulation methods frequently include numerical analysis, partial differential equations and tensor analysis. Multiphysics simulation process The implementation of a multiphysics simulation follows a typical series of steps: * Identify th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Difference Time-domain Method
Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to the associated system of differential equations). Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way. The FDTD method belongs in the general class of grid-based differential numerical modeling methods (finite difference methods). The time-dependent Maxwell's equations (in partial differential form) are discretized using central-difference approximations to the space and time partial derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Model
A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, chemistry and biology to economics, psychology, cognitive science and computer science. The system under study is often a complex nonlinear system for which simple, intuitive analytical solutions are not readily available. Rather than deriving a mathematical analytical solution to the problem, experimentation with the model is done by adjusting the parameters of the system in the computer, and studying the differences in the outcome of the experiments. Operation theories of the model can be derived/deduced from these computational experiments. Examples of common computational models are weather forecasting models, earth simulator models, flight simulator models, molecular protein folding models, and neural network models. See also * Computational cognition * Reversible computing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, ''discretization'' may also refer to modification of variable or category ''granularity'', as when multiple discrete variables are aggregated or multiple discrete categories fused. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Susan L
Susan is a feminine given name, from Persian "Susan" (lily flower), from Egyptian '' sšn'' and Coptic ''shoshen'' meaning "lotus flower", from Hebrew ''Shoshana'' meaning "lily" (in modern Hebrew this also means "rose" and a flower in general), from Greek ''Sousanna'', from Latin ''Susanna'', from Old French ''Susanne''. Variations * Susana (given name), Susanna, Susannah * Suzana, Suzanna, Suzannah * Susann, Suzan, Suzann * Susanne (given name), Suzanne * Susanne (given name) * Suzan (given name) Suzan may refer to: *Suzan Najm Aldeen (born 1973), Syrian actress * Suzan Anbeh (born 1970), German actress * Suzan Rose Benedict (1873–1942), American academic *Suzan Brittan (born 1967), American actress and vocalist * Suzan Çevik (born 1977) ... * Suzanne (other), Suzanne * Suzette (given name) * Suzy (given name) * Zuzanna (given name) *Cezanne (Avant-garde) Nicknames Common nicknames for Susan include: * Sue (other), Sue, Susie (other), Susie, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Volume Method
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics packages. "Finite volume" refers to the small volume surrounding each node point on a mesh. Finite volume methods can be compared and contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations of a solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Difference Method
In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points. Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently which, along with their relative ease of implementation, has led to the widespread use of FDM in modern numerical analysis. Today, FDM are one of the most common approaches to the numerical solution of PDE, along with finite element meth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The simpl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Value Problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interdisciplinarity
Interdisciplinarity or interdisciplinary studies involves the combination of multiple academic disciplines into one activity (e.g., a research project). It draws knowledge from several other fields like sociology, anthropology, psychology, economics, etc. It is about creating something by thinking across boundaries. It is related to an ''interdiscipline'' or an ''interdisciplinary field,'' which is an organizational unit that crosses traditional boundaries between academic disciplines or schools of thought, as new needs and professions emerge. Large engineering teams are usually interdisciplinary, as a power station or mobile phone or other project requires the melding of several specialties. However, the term "interdisciplinary" is sometimes confined to academic settings. The term ''interdisciplinary'' is applied within education and training pedagogies to describe studies that use methods and insights of several established disciplines or traditional fields of study. Inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristic Equation (calculus)
In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree upon which depends the solution of a given th-order differential equation or difference equation. The characteristic equation can only be formed when the differential or difference equation is linear and homogeneous, and has constant coefficients. Such a differential equation, with as the dependent variable, superscript denoting ''n''th-derivative, and as constants, :a_y^ + a_y^ + \cdots + a_y' + a_y = 0, will have a characteristic equation of the form :a_r^ + a_r^ + \cdots + a_r + a_ = 0 whose solutions are the roots from which the general solution can be formed. Analogously, a linear difference equation of the form :y_=b_1y_ + \cdots + b_ny_ has characteristic equation :r^n - b_1r^ - \cdots - b_n =0, discussed in more detail at Linear recurrence with constant coefficients#Solution to homogeneous case. The characteristic roots (roots of the characteristic equation) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Governing Equations
The governing equations of a mathematical model describe how the values of the unknown variables (i.e. the dependent variables) change when one or more of the known (i.e. independent) variables change. Mass balance A mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. It is the simplest governing equation, and it is simply a budget (balance calculation) over the quantity in question: \text + \text = \text + \text \ + \text Differential equation Physics The governing equations in classical physics that are lectured at universities are listed below. * balance of mass * balance of (linear) momentum * balance of angular momentum * balance of energy * balance of entropy * Maxwell-Faraday equation for induced electric field * Ampére-Maxwell equation for induced magnetic field * Gauss equation for electric flux * Gauss equation for magnetic flux Classical continuum mechanics The basic equations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
