A Time-Domain Meshless Method Without Discretization in Time

In this letter, we propose a new time-domain meshless method without discretization in time based on eigenexpansions of numerical solutions. As a result, numerical time-stepping is not required, and its associated errors are eliminated. Analytical solutions of the radial point interpolation meshless (RPIM) method are derived, and the solutions become always stable. In other words, electric and magnetic field values are available at any time, making late-time electromagnetic field analysis convenient and efficient. Numerical experiments are conducted to verify the effectiveness and accuracy of the proposed method.