<button>button</button>

<select id="calc_test__number" multiple="" class="input_error">
  <option value="test123">Test123</option>
  <option value="test321">Test321</option>
  <option value="test234">Test234</option>
  <option value="test432">Test432</option>
</select>

$('button').click(() => {
  $('#calc_test__number').val(["test234","test432"]);
})