Solving linear systems by elimination



When Solving linear systems by elimination, there are often multiple ways to approach it. Math can be a challenging subject for many students.



Solve linear systems by elimination

In algebra, one of the most important concepts is Solving linear systems by elimination. When you encounter a problem, you should take the initiative to find the textbook, find its source, and find out where your problem is. The answers of the open book examination questions can not be found intact in the book, which requires some thinking. Without a firm grasp of basic knowledge, it is difficult to have a complete answer. Moreover, the open book examination has a time limit. To form a correct answer, you need to have time to think.

However, because the equations are solved in a decoupled manner, the convergence speed of the solutions is relatively slow. The method of separating variables is a general method to solve the boundary value problem of Laplace equation. Its main idea is to find a way to convert the partial differential equation with coupled variables into an ordinary differential equation, then find the eigenvalues and eigensolutions respectively, and finally use the superposition principle to get a general solution. Under different coordinate conditions, the methods of separating variables are different, which are described below The analysis of linear continuous time systems can be reduced to the process of establishing and solving linear differential equations.

The transfinite element method is one of the core technologies of the HFSS algorithm. In this method, the field quantity to be solved is expanded with the mode at the port as the basis function, so the field quantity in the solving functional is converted into the expansion coefficient of the solving mode. The S parameter is also solved while solving the field quantity, and no post-processing of the field quantity is required, so it is more accurate. The ultimate goal of using the solver is still to solve practical problems.

The integral equation algorithm of HFSS is based on the integral form of Maxwell's equation, which can automatically meet the radiation boundary conditions. The integral equation is used to solve the full wave of the object to be solved, calculate the current on the surface of the model, and solve the conductor and dielectric models. It has great advantages for simple models and radiation problems of materials. The integral equation solver of HFSS includes two algorithms: We propose a rigid body simulation method, which can solve small time and space details by using an unconditionally stable quasi explicit integration scheme. Traditional rigid body simulators linearize the constraint conditions because they operate at the velocity level or implicitly solve the equations of motion, thus freezing the constraint direction in multiple iterations.

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