{
  "id": "2304.14021",
  "version": "v1",
  "published": "2023-04-27T08:32:01.000Z",
  "updated": "2023-04-27T08:32:01.000Z",
  "title": "Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs",
  "authors": [
    "Gobinda Garai",
    "Bankim C. Mandal"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the nonlinear CH equation. We use diagonalization technique on all-at-once system to develop efficient iterative time parallel methods for investigating the solution behaviour of said equations. We present the convergence analysis of Parallel-in-Time (PinT) algorithms. We verify our findings by presenting numerical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-27T08:32:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N06",
      "65N12",
      "65Y05",
      "65N15",
      "65Y20"
    ],
    "keywords": [
      "fourth order time dependent pdes",
      "parallel-in-time method",
      "time-dependent partial differential equations",
      "efficient time parallel method",
      "order time-dependent partial differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}